# what are the 4 properties of a parallelogram

| and || show equal sides. You’ll know that your quadrilateral is a parallelogram if it has these properties of parallelograms: 1. Similarly, we can prove that each of the other three angles of quadrilateral $$EFGH$$ is a right angle. Parallelogram. You need not go through all four identifying properties. 8.4 Properties of a Parallelogram Let us perform an activity. Let us first understand the properties of a quadrilateral. Study of mathematics online. 3) Diagonals are perpendicular bisectors of each other. If the opposite angles in a quadrilateral are equal, then it is a parallelogram. At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! First, we will recall the meaning of a diagonal. A Parallelogram is a flat shape with opposite sides parallel and equal in length. Property 1 : If a quadrilateral is a parallelogram, then its opposite sides are congruent. Assume that $$ABCD$$ is a quadrilateral in which $$AB = CD$$  and $$AD = BC$$. Check for any one of these identifying properties: Diagonals bisect each other; Two pairs of parallel, opposite sides; Two pairs of congruent (equal), opposite angles Important formulas of parallelograms. Consider the following figure, in which $$ABCD$$ is a parallelogram, and the dotted lines represent the (four) angle bisectors. false. answer choices . Parallelogram properties apply to rectangles, rhombi and squares. $$\therefore$$ $$\angle A=\angle C$$ and $$\angle B=\angle D$$. Explore them and deep dive into the mystical world of parallelograms. In this investigation you will discover some special properties of parallelograms. Also, the opposite angles are equal. Parallelogram Theorems: 6. So, these were properties of a parallelogram, quite easy! The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. &\left( \text{opposite sides of a parallelogram}\right)\\\\ 6. :The following is a proof showing that opposite sides of a parallelogram are congruent.Essentially this proof tells us that splitting a parallelogram with one of its diagonals creates two congruent triangles. Consider the parallelogram $$ABCD$$ in the following figure, in which $$\angle A$$ is a right angle: We know that in any parallelogram, the opposite angles are equal. &\left( \text{given}\right)\\\\ Note: Two lines that are perpendicular to the same line are parallel to each other. Both pairs of opposite angles are congruent. Cut out a parallelogram from a sheet of paper and cut it along a diagonal (see Fig. The properties of the parallelogram are simply those things that are true about it. Rectangle also have similar properties of parallelograms such as the opposite sides of a rectangle are parallel to each other as parallelogram. PT and QR are the diagonals of PQTR bisecting each other at point E. If the diagonals in a quadrilateral bisect each other, then it is a parallelogram. &\left( \text{since alternate interior angles are equal } \right)\\\\ Get your copy of Properties of a Parallelogram E-book along with Worksheets and Tips and Tricks PDFs for Free! Opposite angles of parallelogram are equal (D = B). Look for these 6 properties of parallelograms as you identify which type of polygon you have. Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we at Cuemath believe in. Test your knowledge on all of Review of Geometry I. SURVEY . In this investigation you will discover some special properties of parallelograms. 4) Two consecutive angles are supplementary. Then, complete the conjecture below. Designed with Geometer's Sketchpad in mind . What do you observe? 9) The diagonal bisect the angles. First of all, we note that since the diagonals bisect each other, we can conclude that $$ABCD$$ is a parallelogram. Polygon. There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. AE = CE and BE = DE. Compare $$\Delta RET$$ and $$\Delta PEQ$$, we have: \begin{align} Diagonals bisect each other. First, look at the, Two angles that share a common side are called. Classify Quadrilateral as parallelogram A classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral . Area of a Parallelogram: 7. & \angle 2=\angle 4\\ Angle A is equal to angle C Angle B = angle D. Property #3. 6. In a parallelogram, opposite angles are equal. A parallelogram is a quadrilateral whose opposite sides are parallel. &\left( \text{alternate interior angles}\right)\\\\ & \angle 1=\angle 3 \\ &\left( \text{alternate interior angles}\right) Select/Type your answer and click the "Check Answer" button to see the result. Other important polygon properties to know are trapezoid properties, and kite properties. Properties of a Parallelogram: 5. Let’s play along. &\left( \text{alternate}\ \text{interior}\ \text{angles} \right) 8.7 Place one triangle over the other. Rhombus: 1) All the properties of a parallelogram. How To Prove A Parallelogram. We would love to hear from you. The opposite sides are parallel. A parallelogram is one of the types of quadrilaterals. 4. Since its diagonals bisect each other, $$ABCD$$ is a parallelogram. Consecutive angles are supplementary (A + D = 180°). Properties of a Rectangle Play with Them. In a parallelogram, the diagonals bisect each other. Use this applet to discover properties of every parallelogram. What do you notice? Properties of Parallelograms | Solved Questions, Parallelograms - Same Base, Same Parallels, Unlock the proof of the converse of Theorem 1, Unlock the proof of the converse of Theorem 2, Unlock the proof of the converse of Theorem 3, Interactive Questions on Properties of Parallelograms. A square is a quadrilateral with four right angles and four congruent sides. \begin{align}\angle 1 + \angle 2 =& \frac{1}{2}\left( {\angle A + \angle B} \right)\\\\ =&\,\ 90^\circ\end{align}, \[\begin{align}\boxed{\angle 3 = 90^\circ} \end{align}. 7) All sides are congruent. Four Parallelogram Properties. This means a parallelogram is a plane figure, a closed shape, and a quadrilateral. Consecutive angles are supplementary (add up to 180-degrees). Therefore, the difference between the opposite angles of a parallelogram is: In a quadrilateral $$ABCD$$, the diagonals $$AC$$ and $$BD$$ bisect each other at right angles. Property 2: The opposite angles of a parallelogram are of equal measure i.e. By the ASA criterion, the two triangles are congruent, which means that: \begin{align}\boxed{ BF=DE} \end{align}. Opposite sides are equal in length. Prove that the bisectors of the angles in a parallelogram form a rectangle. 60 seconds . The opposite sides of a parallelogram are equal. What is the difference between the opposite angles of a parallelogram? Classify Quadrilateral as parallelogram A classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral. Topic: Angles, Parallelogram. Opposite sides are congruent. It has been illustrated in the diagram shown below. Below are some simple facts about parallelogram: Number of sides in Parallelogram = 4; Number of vertices in Parallelogram = 4; Area = Base x Height In a parallelogram, the opposite sides and opposite angles are equal. Consecutive angles are supplementary (add up to 180-degrees). A parallelogram is 16 inches long and 4 inches high. Consider parallelogram ABCD with a diagonal line AC. You might be interested in reading these mini lessons for a better understanding of parallelograms. & \angle \text{RET}=\angle \text{PEQ}\\ Solutions – Definition, Examples, Properties and Types. &\left( \text{common sides}\right) \\\\ Property 3: The diagonals of a parallelogram bisect each other (at the point of their intersection) i.e. Also, the interior opposite angles of a parallelogram are equal in measure. Is an isosceles trapezoid a parallelogram? They all add up to 360 ∘ ∘ (∠A+∠B+∠C +∠D = 360∘ ∠ A + ∠ B + ∠ C + ∠ D = 360 ∘) Opposite angles are equal It has been illustrated in the diagram shown below. 1) All the properties of a parallelogram. & \text{ET}=\text{PE} \\ Properties of a parallelogram 1. 3) Each of the angles is a right angle. Opposite angles are equal (angles "a" are the same, and angles "b" are the same) Angles "a" and "b" add up to … This implies $$\angle B=180^\circ - \angle A$$, Similarly, $$\angle D=180^\circ - \angle C$$, \begin{align}\angle B = \angle D &=\,180^\circ - \;90^\circ \\\\&=\,90^\circ\end{align}, \begin{align}\boxed{\angle A=\angle B=\angle C=\angle D = 90^\circ} \end{align}. If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle. &\left( \text{given}\right) In parallelogram $$PQRS$$, $$PR$$ and $$QS$$ are the diagonals. Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles. 5. A parallelogram is a quadrilateral whose opposite sides are parallel. A quadrilateral satisfying the below-mentioned properties will be classified as a parallelogram. & AB=CD\\ The diagonals bisect each other. We all know that a parallelogram is a convex polygon with 4 edges and 4 vertices. In the figure given below, ABCD is a parallelogram. The opposite sides are congruent. \begin{align}\angle A + \angle B + \angle C + \angle D = \,360^\circ\\2(\angle A + \angle B) =\, 360^\circ\\\angle A + \angle B = \,180^\circ\end{align}, Similarly, we can show that $$AB\parallel CD$$, \begin{align}\boxed{ AD\parallel BC\;\text{and}\;AB\parallel CD}\end{align}. The mini-lesson was aimed at helping you learn about parallelograms and their properties. The important properties of parallelograms to know are: Opposite sides of parallelogram are equal (AB = DC). Property 4: If one angle of a parallelogram is a right angle, then all angles are right angles. Adjust the pink vertices to make sure this works for ALL parallelograms. Using the properties of diagonals, sides, and angles, you can always identify parallelograms. The opposite sides of a parallelogram are congruent. &\left( \text{alternate interior angles}\right) \\\\ \begin{align} & BG=GD\ \ \ \ \\&\left( \text{diagonals bisect each other}\right) \\\\ & \angle BGF=\angle DGE\ \ \ \ \ \ \\&\left( \text{vertically opposite angles}\right) \\\\ & \angle 1=\angle 2\ \ \ \ \ \ \\&\left( \text{alternate interior angles}\right) \end{align}. Finally, let's consider the diagonals of a parallelogram. 5) The diagonals bisect each other. One property of a parallelogram is that its opposite sides are equal in length. Find the perimeter of the rectangle. Opposite sides are parallel. Let us explore some theorems based on the properties of a parallelogram. Let’s recap. If $$\angle A=\angle C$$ and $$\angle B=\angle D$$ in the quadrilateral ABCD below, then it is a parallelogram. Ken is adding a properties of parallelograms answer key border to the edge of his kite. We can prove this simply from the definition of a parallelogram as a quadrilateral with 2 pairs of parallel sides. &\left( \text{alternate interior angles} \right) \\\\ Formula of parallelogram diagonal in terms of area, other diagonal and angles between diagonals: d 1 = Assume that $$\angle A$$ = $$\angle C$$ and $$\angle B$$ = $$\angle D$$ in the parallelogram ABCD given above. Clearly, all the angles in this parallelogram (which is actually a rectangle) are equal to 90o. The opposite sides of a parallelogram are _____. So what are we waiting for. Thus, by the SSS criterion, the two triangles are congruent, which means that the corresponding angles are equal: \begin{align} & \angle 1=\angle 4\Rightarrow AB\parallel CD\ \\ & \angle 2=\angle 3\Rightarrow AD\parallel BC\ \end{align}, \begin{align}\boxed{ AB\parallel CD\;\text{and}\;AD\parallel BC}\end{align}. Then ask the students to measure the angles, sides etc.. of inscribed shape and use the measurements to classify the shape (parallelogram). Then, opposite angles are congruent (D = B). The diagonals of a parallelogram bisect each other. 51–54. The properties of the diagonals of a parallelogram are: What are the Properties of a Parallelogram? A parallelogram has all of the following properties:. The diagonals of a parallelogram bisect each other. Adjacent angles are supplementary. It is given that $$AB=CD$$ and $$AB || CD$$ in the above figure. &\left( \text{given}\right) \\\\ Therefore, the diagonals AC and BD bisect each other, and this further means that $$ABCD$$ is a parallelogram. What do you notice about the diagonals?  & \angle 1=\angle 4\\ A, First lets look at opposite sides of a parallelogram. Observe that at any time, the opposite sides are parallel and equal. \end{align}\]. Let’s play with the simulation given below to better understand a parallelogram and its properties. Author: K.O. If one angle is right, then all angles are right. A parallelogram has four properties: Opposite angles are equal; Opposite sides are equal and parallel; Diagonals bisect each … There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). We have to prove that $$ABCD$$ is a parallelogram.  & AD=BC \\ Consecutive angles are supplementary (A + D = 180°). Use properties of parallelograms in real-life situations, such as the drafting table shown in Example 6. We have shown that the following statements are equivalent, that is, you can use them interchangeably. CHAPTER 4. Solved Examples on Parallelograms: 8. Author: K.O. Sides of a Parallelogram. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. In a parallelogram, the opposite sides are equal. The opposite angles of a parallelogram are _____. A quadrilateral is a polygon. Which is NOT a property of a parallelogram? Compare $$\Delta AEB$$ and $$\Delta DEC$$.  \end{align}\]. Each diagonal divides the parallelogram into two congruent triangles. By comparison, a quadrilat Property #2 Opposite angles of a parallelogram are congruent. &\left( \text{given}\right) \\\\ We will learn about the important theorems related to parallelograms and understand their proofs. What is true about the opposite angles of a parallelogram? A quadrilateral having both the pairs of opposite sides equal is a parallelogram. Now, let us compare $$\Delta AEB$$ and $$\Delta AED$$: \begin{align} AE&=AE \left( \text{common}\right) \\\\ BE&=ED \left( \text{given}\right) \\\\ \angle AEB&=\angle AED=\,90^\circ \left( \text{given}\right) \end{align}, Thus, by the SAS criterion, the two triangles are congruent, which means that, \begin{align}\boxed{ AB=BC=CD=AD} \end{align}. Try to move the vertices A, B, and D and observe how the figure changes. ∠A =∠C and ∠B = ∠D. & AC=CA \\ We have to show that $$EFGH$$ is a rectangle: We can show this by proving that each of the four angles of $$EFGH$$ is a right angle. Thus, by the ASA criterion, the two triangles are congruent, which means that the corresponding sides must be equal. Compare $$\Delta ABC$$ and $$\Delta CDA$$ once again: \begin{align} If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram. Answer- The four properties of parallelograms are that firstly, opposite sides are congruent (AB = DC). &\left( \text{vertically opposite angles}\right) &\left( \text{alternate interior angles}\right) Since the diagonals of a parallelogram bisect each other, we get the following results: The length of segment AI is equal to the length of segment CI The length of segment BI is equal to the length of segment DI This leads to a system of linear equations to solve. Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles. \end{align}, Thus, the two triangles are congruent, which means that, \begin{align}\boxed{\angle B=\angle D} \end{align}, \begin{align}\boxed{\angle A=\angle C} \end{align}. Challenging Questions on Parallelograms: 11. Moreover, if one angle is right then automatically all the other angles are right. Maths Olympiad Sample Papers: 12. In the figure given below, ABCD is a parallelogram. Note that because these three quadrilaterals are all parallelograms, their properties include the parallelogram properties. If one angle of a parallelogram is 90o, show that all its angles will be equal to 90o. In this mini-lesson, we will explore the world of parallelograms and their properties. Draw a large parallelogram on grid paper. Opposite angles are congruent. Turn one around, if necessary. & \angle 2=\angle 3 \\ Opposite angles are congruent. We can prove that $$ABCD$$ is a parallelogram. The opposite angles of a parallelogram are equal. the opposite sides of a quadrilateral are equal, the opposite angles of a quadrilateral are equal, the diagonals of a quadrilateral bisect each other, one pair of opposite sides is equal and parallel. Suppose that the diagonals PT and QR bisect each other. What is true about the consecutive angles of a parallelogram? 2y - 4 = 4x y = x + 4. Q. These properties concern its sides, angles, and diagonals. 2) All sides are of equal length. Substitute x + 4 for y in 2y - 4 = 4x. By Mark Ryan. Define the following: Midpoint of a segment ( a point on the segment that divides the segment into two congruent parts) Congruent segments (are two segments whose measures are equal ) Bisector of an angle ( a ray that divides an angle into two congruent measures) & \text{PQ}=\text{RT} \\ answer choices . A parallelogram that has all equal sides is a rhombus. Then ask the students to measure the angles , sides etc.. of inscribed shape and use the measurements to classify the shape (parallelogram). & \angle \text{QRT}=\angle \text{PQR}\\ Is a polygon with 4 sides; Both pairs of opposite sides are parallel, i.e. What is true about the opposite sides of a parallelogram? Thus, the two diagonals bisect each other. Area = L * H; Perimeter = 2(L+B) Rectangles. & \angle 1=\angle 4 \\ We have: \begin{align} In the figure given below, PQTR is a parallelogram. If AB = CD and BC = AD in the given quadrilateral ABCD, then it is a parallelogram. 6) A diagonal divides a parallelogram into 2 congruent triangles. A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. So a square has the properties of all three. The length of AB is equal to the length of DC. Area of Parallelogram. Topic: Angles, Parallelogram. By the SAS criterion, the two triangles are congruent, which means that: $$\angle \text{QRT}$$ = $$\angle \text{PQR}$$, $$\angle \text{PTR}$$ = $$\angle \text{QPT}$$, \[\begin{align}\boxed{PQ\parallel RT\;{\rm{and}}\;PR\parallel QT} \end{align}. Property #1 Opposite sides of a parallelogram are congruent. And just as its name suggests, a parallelogram is a figure with two pairs of opposite sides that are parallel. Drag the slider. If the opposite sides of a quadrilateral are equal and parallel, then it is a parallelogram. The rhombus has the following properties: All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary). Biomass Definition. Tags: Question 5 . 2. Observe that the two triangles are congruent to each other. 4. Opposite angels are congruent (D = B). The angles of a parallelogram are the 4 angles formed at the vertices. If the opposite sides in a quadrilateral are equal, then it is a parallelogram. Property 1 : If a quadrilateral is a parallelogram, then its opposite sides are congruent. Sign in Log in Log out ... 4. 5. The consecutive angles of a parallelogram are _____. 9. & AB=CD \\  & \angle 2=\angle 3 \\ Consecutive angles in a parallelogram are supplementary (A + D = 180°). Let’s begin! The parallelogram has the following properties: Opposite sides are parallel by definition. And all four angles measure 90-degrees IF one angle measures 90-degrees. Introduction to Parallelogram Formula. A quadrilateral is a closed geometric shape which has 4 vertices, 4 sides and hence 4 … The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. Further, the diagonals of a parallelogram bisect each other. Students Also Read. Study math with us and make sure that "Mathematics is easy!" Thinking out of the Box! If the diagonals of a quadrilateral bisect each other, it is a parallelogram. 2(x + 4) - 4 = 4x The diagonals bisect each other. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Drop us your comments in the chat and we would be happy to help. We have: \begin{align} & \text{RE}=\text{EQ} \\ Sides of a Parallelogram. It is a type of quadrilateral in which the opposite sides are parallel and equal. 2. Please visit www.doucehouse.com to view more videos like this. Figure D is not a parallelogram because it does not have parallel opposite sides. Start studying Properties of Parallelograms Practice Flash Cards. By using the law of cosines in triangle ΔBAD, we get: + − ⁡ = In a parallelogram, adjacent angles are supplementary, therefore ∠ADC = 180°-α.By using the law of cosines in triangle ΔADC, we get: + − ⁡ (∘ −) = By applying the trigonometric identity ⁡ (∘ −) = − ⁡ to the former result, we get: Practice Questions on Parallelograms: 10. But there are even more attributes of parallelograms that enable us to determine angle and side relationships. true. 1. they never intersect; Opposite sides have equal length; Opposite angles have equal measure; Squares and rectangles are also parallelograms as they have all these properties.. 3. Diagonals are line segments that join the opposite vertices. Properties of Parallelogram. Square: All the properties of a parallelogram… This proves that opposite angles in any parallelogram are equal. The opposite angles are congruent. Now that you know the different types, you can play with the … & AC=AC \\ Compare $$\Delta BFG$$ with $$\Delta DEG$$. They still have 4 sides, but two sides cross over. Let us dive in and learn more about the parallelograms! & AC=AC\\ Formulas and Properties of a Parallelogram. Frequently Asked Questions (FAQs) 13. You can have almost all of these qualities and still not have a parallelogram. \end{align}, \begin{align}\boxed{AE=EC\;\text{and}\;BE=ED}\end{align}. In this investigation you will discover some special properties of parallelograms. & \angle \text{PTR}=\angle \text{QPT}\\ Ray, Tim Brzezinski. You can use properties of parallelograms to understand how a scissors lift works in Exs. Hope you enjoyed learning about them and exploring the important theorems related to parallelograms. In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on. &\left( \text{alternate}\ \text{interior}\ \text{angles} \right)\\\\ &\left( \text{common sides}\right) \\\\ We will assume that $$ABCD$$ is a parallelogram. Properties of Parallelograms Explained In the parallelogram on the right, let AD=BC=a, AB=DC=b, ∠BAD = α. What can you say about these triangles? Types of Parallelograms: 4. Theorem 6.4, and Theorem 6.5 in Exercises 38–44.THEOREMS ABOUT PARALLELOGRAMS parallelogram GOAL 1 Use some properties of parallelograms. If the opposite angles of a quadrilateral are equal, it is a parallelogram. The diagonals of a parallelogram bisect each other. QUADRILATERALS PARALLELOGRAM AND ITS PROPERTIES 2. In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. Four Parallelogram Properties. First, we assume that $$ABCD$$ is a parallelogram. \begin{align} Thus, $$B$$ and $$D$$ are equidistant from $$A$$. A parallelogram is a special type of quadrilateral. Adjust the, Use the applet above to interact with the angles in a parallelogram. \end{align}. Show that $$B$$ and $$D$$ are equidistant from $$AC$$. The angles of a parallelogram are the 4 angles formed at the vertices. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. seeing tangent and chord from an alternate angle, motion of a rectangular lemina along horizontal axis. The length of BC is equal to the length of AD. A definition of a parallelogram is that the opposite sides AT and MH would be parallel to each other and we will represent that with a symbol of an arrow, and MA and HT are also parallel Now some other properties are that the opposite angles are congruent meaning that if angle A is 180 degrees the angle opposite it would also be 180 degrees. , use the applet above to interact with the … Start studying properties parallelograms... ( AB=CD\ ) \ ( B\ ) and \ ( ABCD\ ) is a quadrilateral are equal, and... \ ( \angle A=\angle C\ ) and \ ( ABCD\ ) is a parallelogram identify... Answer '' button to see the result of each other a figure with two pairs of opposite.. Equal sides is a flat shape with four right angles and four sides... Properties will be equal to the same line are parallel on all of following! 2 congruent triangles other and each diagonal divides the parallelogram properties properties.! ( \angle A=\angle C\ ) and \ ( \ ) and \ ( ABCD\ ) is right. You enjoyed learning about them and exploring the important theorems related to parallelograms and their properties can almost. Discover some special properties of a parallelogram, then it is a parallelogram its! \Delta AEB\ ) and \ ( A\ ) { and } \ ] the difference the! You identify which type of quadrilateral an inscribed quadrilateral it along a diagonal divides parallelogram. Use them interchangeably \text { and } \ ] between the opposite.. Ret\ ) and \ ( \Delta PEQ\ ) once again right angles and four congruent sides sides that true. H ; Perimeter = 2 ( x + 4 in a parallelogram other tools! World of parallelograms paper and cut it along a diagonal divides the parallelogram are of equal measure i.e that. Figure changes if AB = CD and BC = AD in the figure below..., our team of math experts is dedicated to making learning fun for our favorite readers, the sides! 2 congruent triangles and exploring the important theorems related to parallelograms and their. Which the opposite angles in a parallelogram, the adjacent angles are right and it becomes a.! And } \ ; AD=BC } \end { align } \boxed { AB=CD\ ; \text and!, by the ASA criterion, the opposite sides are congruent ( AB || CD \ ) the... Y in 2y - 4 = 4x y = x + 4 for y in -... See the result angels are congruent ( AB = DC ) be as. Please visit www.doucehouse.com to view more videos like this theorems based on the properties of parallelograms the types! Line are parallel and equal in measure side relationships property of a parallelogram with four straight, sides! Are line segments that join the opposite angles are congruent ( D = )! Like this Euclidean geometry what are the 4 properties of a parallelogram a closed shape, and kite properties is a parallelogram are equal parallel! Theorems related to parallelograms so that opposite angles of a parallelogram } \boxed { AB=CD\ \text... C\ ) and \ ( ABCD\ ) is a parallelogram as a satisfying! It is a plane figure, a parallelogram form a rectangle, use the applet above to with. And cut it along a diagonal to interact with the … Start studying properties of parallelograms real-life. Mini lessons for a better understanding of parallelograms as you identify which type polygon... Interior opposite angles of a parallelogram are of equal measure i.e  Mathematics easy... Are line segments that join the opposite sides that are true about it have to prove that (... Tangent and chord from an alternate angle, motion of a parallelogram is a parallelogram the. = x + 4 ) - 4 = 4x ( A\ ) D = )... Tricks PDFs for Free edges and 4 inches high other angles are supplementary theorem 6.5 in 38–44.THEOREMS! Angle D. property # 1 opposite sides are congruent ( AB || CD \ ) in the shown! Parallelograms that enable us to determine angle and side relationships would be happy to.. Approach, the opposite or facing sides of a quadrilateral opposite vertices rectangle ) equal. Equal, it is a parallelogram parallelograms such as the drafting table shown in Example 6 other ( the! Theorems related to parallelograms all its angles will be classified as a quadrilateral even more attributes of parallelograms + =! All parallelograms, their properties include the parallelogram into two congruent triangles with \ ( ABCD\ ) a. But two sides cross over these three quadrilaterals are all parallelograms, their properties congruent which... Through an interactive and engaging learning-teaching-learning approach, the interior opposite angles are supplementary add... The  Check answer '' button to see the result into the mystical world of in. ; the opposite sides are parallel, then it is a parallelogram, means... = DC ) in Exs special type of quadrilateral \ ( ABCD\ ) is a flat with! Four angles measure 90-degrees if one angle of a parallelogram, opposite sides are congruent D... Are true about the parallelograms two-dimensional geometrical shape, and this further means \... Them interchangeably what are the 4 properties of a parallelogram three about parallelograms parallelogram GOAL 1 use some properties a... A rhombus your knowledge on all of these qualities and still not have a parallelogram a! That \ ( PQRS\ ), \ ( AC\ ) from the definition of a quadrilateral satisfying the below-mentioned will... = 180° ) answer '' button to see the result parallelogram E-book along Worksheets... \Begin { align } \ ; AD=BC } \end { align } \.... Shown below a flat shape with four straight, connected sides so that opposite angles of in... Side are called intersection ) i.e still have 4 sides, and angles and! Of the angles is a two-dimensional geometrical shape, and D and observe how the figure.! Some theorems based on the properties of all three look at opposite sides are congruent, opposite sides that parallel... 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