In the figure, ABCD is parallelogram and AP = CQProve that PBQD is a p

1.	In the figure, ABCD is parallelogram and AP = CQProve that PBQD is a parallelogram
Answer» DC = AB ………. (1) AD = CB QC = AP ……. (2) (as ABCD is a parallelogram) (1) – (2) ⇒ DC – QC = AB – AP; ∴ DQ = PB When, ∆ APD, ∆ CQB are considered. AD = CB AP = QC ∠A = ∠C, The two sides and angle formed by them in these triangles are equal. So the third sides PD and BQ are equal. ∴ Two pairs of opposite sides in the quadrilateral PBQD are equal. So PBQD is a parallelogram.

In the figure, ABCD is parallelogram and AP = CQProve that PBQD is a parallelogram

Answer»

DC = AB ………. (1)

AD = CB

QC = AP ……. (2) (as ABCD is a parallelogram)

(1) – (2) ⇒ DC – QC = AB – AP;

∴ DQ = PB When, ∆ APD, ∆ CQB are considered.

AD = CB

AP = QC

∠A = ∠C, The two sides and angle formed by them in these triangles are equal. So the third sides PD and BQ are equal.

∴ Two pairs of opposite sides in the quadrilateral PBQD are equal. So PBQD is a parallelogram.