Question

the bisector of the angle B of the triangle ABC , right angled at A meets the altitude AP at X and the side AC at Y. Prove that AC*AY = AP*CY​

Answer 1

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.

2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that

(i) ΔABD ≌ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.