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ICSE Class 9 Answered

In a triangle ABC,the bisector of the angle BCA, meets AB in X.A point Y lies on CX such that AX =AY.Prove  that angle CAY = angle ABC
Asked by Rp1298908 | 24 Oct, 2018, 07:30: PM
answered-by-expert Expert Answer
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)
∠AYX + ∠AYC = ∠AXY + ∠BXY......both are linear pairs
from (2)
∠AYC = ∠BXY.......(3)
In Δ AYC and ΔBXC 
Δ AYC ~ ΔBXC.....AA test
∠CAY = ∠XBC......... c.p.s.t.
∠CAY = ∠ABC
Answered by Arun | 25 Oct, 2018, 11:57: AM

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