Complete the following activity to prove ABCD parallelogram. Given: In QABCD, Seg CB = Seg DA and Seg CB || Seg DA To Prove: OABCD is a parallelogram. С Construction: Draw diagonal BD. Proof: ACBD=AADB- B. A .. ZCDB प .:. Seg CD Seg BA—alternate angles test for parallel lines.) :. []'ABCD is a parallelogram.
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Answer:
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Class 9
>>Maths
>>Quadrilaterals
>>Properties of a Parallelogram
>>Proving Properties of Paral...
Proving Properties of Parallelogram
Maths
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DEFINITION
opposite angles of parallelogram are congruent
concept
Diagonal of Parallelogram: Parallelogram is a Quadrilateral whose both pairs of opposite sides are parallel and equal. In a parallelogram, the Diagonals Bisect one another. One pair of opposite sides is Parallel and Equal in length.
Given: □PQRSis a Parallelogram.
To prove: ∠SPQ≅∠QRS
and ∠PSR≅∠RQP
Construction: Draw a diagonal SQ
Proof: □PQRS is a parallelogram.
∴sidePS∣∣sideQR and seg SQ is a transveral
∴∠PSQ≅∠RQS ...(Alternate angles) ...(1)
Also, sidePQ∣∣sideSR and seg SQ is a transversal.
∠PQS≅∠RSQ ...(Alternate angles)...(2)
In △PQS and △RSQ
∠PSQ≅∠RQS ...from (1)
sideSQ≅sideQS ...(common side)
∠PQS≅∠RSQ ...from (2)
∴△PQS≅△RSQ ...(ASA test)
∴∠SPQ≅∠QRS ...(c.a.c.t.)
Similarly, we can prove by drawing diagonal PR.
∠PSR≅∠RQP
Hence, the opposite angles of a parallelogram are congruent.
Answer:
1) Given: In ABCD, Seg CB cong segDA and segCB ||seg DA
23
seg BA (D) (angles test for parallel lines)
..ABCD is a parallelogram.........from given and (1)
Proof: Delta boxed DB cong Delta*ADB - (SAStest)
angle CDB cong angle ABD
Complete the following proof.
seg
Construction: Draw diagonal BD.
To prove ABCD is a parallelogram