Question

X and Y are two points on equal sides AB and AC of a triangle ABC such that AX=AY prove that XC=YB

Answer 1

ANSWER

Given: X and Y are two points on equal sides AB and AC of a ∆ABC such that AX = AY.

To Prove: XC = YB

Proof: In ∆ABC,

∵ AB = AC | Given

∴ ∠ABC = ∠ACB ...(1)

| Angles opposite to equal sides of a triangle are equal

Again, AB = AC | Given

AX = AY | Given

Subtracting, we get,

AB - AX = AC - AY

⇒ BX = CY ...(2)

In ∆BXC and ∆CYB,

BX = CY | From (2)

BC = CB | Common

∠XBC = ∠YCB | From (1)

∴ ∆BXC ≅ ∆CYB

| SAS congruence rule

∴ XC = YB | CPCT

Answer 2

Answer:

Hello there !!

Given :-

AX = AY

In ΔAXC and ΔAYB ,

AX = AY [ Given ]

BC = AB [ Given ]

∠A = ∠A [ Common ]

ΔAXC ≅ ΔAYB [ SAS ]

Hence ,

XC = YB [ cpct ]

-----> Proved !!!