In the given figure AE bisects ext angle CAD and AE is parallel to BC - Maths - Congruency of Triangles

Question

In the given figure AE bisects ext angle CAD and AE is parallel to
BC

Neha Sethi · Accepted Answer

Given: AE bisects ∠CAD⇒∠x=∠y  
1and AE∥BCNow  AE∥BC and AC is a transversal
⇒∠EAC=∠ACB⇒y=∠ACBAlso DB is a straight line ⇒∠DAE+∠EAC+∠CAB=180°  Linear pair⇒x+y+∠CAB=180°⇒∠CAB=180°-x-yConsider △ABC, by angle sum property of △∠ABC+∠ACB+CAB=180°⇒∠ABC+y+180°-x-y=180°⇒∠ABC=xSo, ∠ABC=x and ∠ACB=yBut from 1,  ∠x=∠y i
e , ∠ABC=∠ACB⇒AB=AC   sides opposite to equal angles are equal
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