By the converse of isosceles triangle theorem, we have proven that AB ≅ CB
From the question, we are to proof that AB ≅ CB. That is, we are to proof that line AB is congruent to line CB
From the diagram,
∠2 ≅ ∠3 (<em>Vertical angles theorem</em>)
From the given information, we have that
∠1 ≅ ∠2
By the substitution property of equality, we can conclude that
∠1 ≅ ∠3
This means ∠1 is congruent to ∠3
This also means ΔABC is an isosceles triangle with base angles 1 and 3.
By the Converse of isosceles triangle theorem which states "If two angles of a triangle are congruent , then the sides opposite to these angles are congruent."
The side opposite ∠1 is CB and the side opposite ∠3 is AB
∴ AB ≅ CB
Hence, by the converse of isosceles triangle theorem, we have proven that AB ≅ CB
Learn more on Converse of isosceles triangle theorem here: brainly.com/question/27872429
#SPJ1
