Question

Which would prove that △ABC ~ △XYZ? Check all that apply.

Answer 1

Answer:

Correct options,

a) $\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

c) $\frac{AC}{XZ}=\frac{BA}{YX}$ and ∠A = ∠X

Step-by-step explanation:

 Given : ΔABC ≅ Δ XYZ

We have choose out of given options that correctly prove that ΔABC ≅ Δ XYZ

 

Two triangles are said to be similar when their corresponding  sides are in same ratio and the measure of their corresponding angles are equal.

That is $\frac{AB}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

and ∠ A = ∠X , ∠ B = ∠Y AND ∠C = ∠Z

Also ,

We have conditions for two triangle to be similar.

1) SSS : When the ratio of all the three sides of a triangle are equal.

that is $\frac{AB}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

2) SAS: When the ratio of two corresponding sides are equal and the measure of angle between those sides are equal

$\frac{AB}{YX}=\frac{AC}{XZ}$ and ∠ A = ∠X

Thus, Out of given options,

a) $\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

c) $\frac{AC}{XZ}=\frac{BA}{YX}$ and ∠A = ∠X

Answer 2

the correct answers are 1 and 3