Question

Q1. Show that BY=AZ
Q2. Prove that AB=AC​

Answer 1

Answer:

1.  Shown that BY = AZ

2. Proven that AB = AC

Step-by-step explanation:

1. In ΔXYZ, XY = ZX and AX = BX

Between ΔAZX and ΔBYX:

AX = BX, ZX = XY and the Angle between them is common ∠X

∴ ΔAZX ≅ ΔBYX

∴ AZ = BY meaning BY = AZ

2. In the given figure:

AD = AE  ∴ ∠ADE = ∠AED . . . . . . . . . . . . . . (i)

Also, given that, ∠BAD = ∠CAE . . . . . . . . . (ii)

Now ∠ABD = ∠ADE - ∠BAD [∵∠ADE is exterior Angle of ΔABD]

                   = ∠AED - ∠CAE  [using equation (i) and (ii)]

                   = ∠ACE [∵∠AED is exterior Angle of ΔACE]

∴ ∠ABC = ∠ACB

∴ ΔABC is isosceles, meaning AB = AC