Answer with explanation:
Given: △ABC is an isosceles triangle with legs AB and AC.Also, △A Y X is also an isosceles triangle with legs A Y and AX.
To Prove: △ABC ~ △A Y X
Proof with Statement
1. △ABC is isosceles with legs AB and AC; △A Y X is also isosceles with legs A Y and AX.
2.AB ≅ AC and A Y ≅ AX.→definition of isosceles triangle
3.AB = AC and A Y = AX →→ definition of Congruency.
4.→→A Y × AC=AX × AC⇒[Multiplication property of equality]
5.≡A Y × AC=AX × AB⇒[Substitution property of equality]
[tex]6.\rightarrow\frac{AB}{AY}=\frac{AC}{AX}[/tex]
----------------[Division property of equality]
7.Also, ∠A is common angle between two triangles.That is,
∠A=∠A------------[Reflexive property]
⇒Missing statement and Reason in the entire proof.
8.△ABC ~ △AYX----[SAS]
