in Triangle ABC, the bisector of angle BCA meets AB in X. A point Y lies on CX such that AX=AY. Prove that angle CAY= angle ABC
Answers
Answered by
67
In ΔABC, CX is the angle bisector of ∠C
∠ACY = ∠BCX --- (1)
and AX = AY
So in Δ AXY
∠AXY = ∠AYX these are the angles which are opposite to equal sides -- (2)
Now ∠XYC = ∠AXB = 180° this is a straight line
∠AYX + ∠AYC = ∠AXY + ∠BXY
∠AYC + ∠BXY this is taken from 2 and now this will become the equation 3
Also in Δ AYC and ΔBXC
∠AYC + ∠YCA + ∠CAY = ∠BXC + ∠BCX + ∠XBC = 180°
∠CAY = ∠XBC this is taken from 1 and 3
∠CAY = ∠ABC
Answered by
26
hope it helps
mark it as brainliest answer
Attachments:

Similar questions