Question

△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?

Answer 1

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]

$6.\rightarrow\frac{AB}{AY}=\frac{AC}{AX}$

----------------[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]

Answer 2

Answer:

∠A ≅ ∠A; reflexive property

Step-by-step explanation: