Question

Which would prove that ΔABC ~ ΔXYZ? Select TWO options.

Answer 1

Answer:

Answer is the first and third option.

Step-by-step explanation:

Just took the quiz and got it right

Answer 2

Answer:

$\frac{BA}{YX}=\frac{BC}{YZ}$, ∠C ≅∠Z

$\frac{AC}{XZ}=\frac{BA}{YX}$, ∠A≅∠X

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

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

In this problem

The corresponding sides are

BA and YX  

BC and YZ

AC and XZ

The corresponding angles are

∠A and ∠X

∠B and ∠Y

∠C and ∠Z

so

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

and

∠A≅∠X

∠B≅∠Y

∠C ≅∠Z

therefore

$\frac{BA}{YX}=\frac{BC}{YZ}$, ∠C ≅∠Z

$\frac{AC}{XZ}=\frac{BA}{YX}$, ∠A≅∠X

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