# proving the parallelogram side theorem

0000104960 00000 n There are five ways in which you can prove that a quadrilateral is a parallelogram. Properties of parallelogram: Opposite sides of parallelogram are equal . Points A, B, C, and D form a parallelogram. This Lesson (Proof of Opposite sides of a parallelogram are equal) was created by by chillaks(0) : View Source, Show About chillaks : am a freelancer In this lesson we will prove the basic property of a parallelogram that the opposite sides in a parallelogram are equal. Consider the following figure: Proof: In $$\Delta ABC$$ and $$\Delta CDA$$, \[\begin{align} We have a side in between that's going to be congruent. Another interesting, and useful, feature of parallelograms tells us that any angle of the parallelogram is supplementary to the consecutive angles on either side of it. In the video below: We will use the properties of parallelograms to determine if we have enough information to prove a given quadrilateral is a parallelogram. View solution. From the above theorem, it can be decided that if one angle of a parallelogram is a right angle (that is equal to 90 degrees), then all four angles are right angles. You can use these and other theorems in this lesson to prove So we know from the previous video that that side is equal to that side. Use the provided diagrams to help you with the proof. Angles BCA and DAC are congruent by the same theorem. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent. PROVING A THEOREM Prove the Parallelogram Diagonals Converse Theorem 7.10 ) Given Diagonals $\overline{JL}$ and $\overline{\mathrm{KM}}$ bisect each other. 0000118607 00000 n E-learning is the future today. The second angle pair you’d need for ASA consists of angle DHG and angle FJE. The converses of the theorems are stated below. Parallelogram Theorems 1. Theorems. You can use GeoGebra to show that the converse of the mid-point theorem is true. Prove the theorem : Parallelogram on the same base and between the same parallels are equal in area. The converse of this theorem states: If a line is drawn through the mid-point of a side of a triangle parallel to the second side, it will bisect the third side. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the polygon is a parallelogram, this will save time when working a proof.. It has been illustrated in the diagram shown below. m or m2) is a positive real number ... THEOREM – 3: Prove that parallelogram and a rectangle on the same base and between the same parallels are equal in area. Notice how one theorem is the _____ of the other. Which sentence accurately completes the proof? given 2. Theorem. Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem. First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles. ∎ Theorem 4 . Here is a summary of the steps we followed to show a proof of the area of a parallelogram. This geometry video tutorial provides a basic introduction into two column proofs with parallelograms. There is a standard square region of side 1 metre, called a square metre, which is the unit of area measure. Reason- parallelogram side theorem 0000035641 00000 n 0000045848 00000 n 0000099782 00000 n The only shape you can make is a parallelogram. Parallelogram Theorems 2 A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. Prove that both pairs of opposite sides are congruent. Theorem 2. Use the right triangle to turn the parallelogram into a rectangle. Given a parallelogram, you can use the Parallelogram Opposite Sides Theorem (Theorem 7.3) and the Parallelogram Opposite Angles Theorem (Theorem 7.4) to prove statements about the sides and angles of the parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other. Cut a right triangle from the parallelogram. Solution: A Parallelogram can be defined as a quadrilateral whose two s sides are parallel to each other and all the four angles at the vertices are not 90 degrees or right angles, then the quadrilateral is called a parallelogram. PROVING A THEOREM Prove the Parallelogram Diagonals Converse Theorem 7.10 ) Given Diagonals \\overline{JL} and \\overline{\\mathrm{KM}} bisect each other. From the congruency of ΔCFE and ΔADE, we also have DE=EF, and since DF= BC as opposite sides in a parallelogram, DE is half of BC. Pair you ’ d need for ASA consists of angle DHG and angle FJE parallelogram on same! 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