In the figure, P is the midpoint of AB and CD. a) Which angle has the

1.	In the figure, P is the midpoint of AB and CD. a) Which angle has the same measure as that of angle APC ? b) Prove that AC = BD . c) Prove that BD is parallel to AC B A
Answer» . In quadrilateral ABCD we have AC = AD and AB being the bisector of ∠A. Now, in ΔABC and ΔABD, AC = AD [GIVEN] AB = AB [Common] ∠CAB = ∠DAB [∴ AB bisects ∠CAD] ∴ USING SAS criteria, we have ΔABC ≌ ΔABD. ∴ CORRESPONDING parts of congruent TRIANGLES (c.p.c.t) are equal. ∴ BC = BD.

In the figure, P is the midpoint of AB and CD. a) Which angle has the same measure as that of angle APC ? b) Prove that AC = BD . c) Prove that BD is parallel to AC B A

Answer»

. In quadrilateral ABCD we have

AC = AD

and AB being the bisector of ∠A.

Now, in ΔABC and ΔABD,

AC = AD

[GIVEN]

AB = AB

[Common]

∠CAB = ∠DAB [∴ AB bisects ∠CAD]

∴ USING SAS criteria, we have

ΔABC ≌ ΔABD.

∴ CORRESPONDING parts of congruent TRIANGLES (c.p.c.t) are equal.

∴ BC = BD.

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In the figure, P is the midpoint of AB and CD. a) Which angle has the same measure as that of angle APC ? b) Prove that AC = BD . c) Prove that BD is parallel to AC B A​

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In the figure, P is the midpoint of AB and CD. a) Which angle has the same measure as that of angle APC ? b) Prove that AC = BD . c) Prove that BD is parallel to AC B A