Question

which statement about the two triangles shown below is true?

(image of two triangles with vertices x, w, y and z, v, y. sides: xy=2, yz=3, wy=2.5, vy=3.75)

choose the correct answer.

a) the triangles are not similar.

b) the triangles are similar by aa similarity.

c) the triangles are similar by sas similarity.

d) the triangles are similar by sss similarity.

Explanation:

Step1: Identify Vertical Angles

Vertical angles at \( Y \) are equal, so \( \angle XYW \cong \angle ZYV \).

Step2: Check Side Ratios

Calculate ratios of corresponding sides:
\( \frac{XY}{ZY} = \frac{2}{3} \), \( \frac{WY}{VY} = \frac{2.5}{3.75} = \frac{2}{3} \).

Step3: Apply SAS Similarity

Two sides in proportion (\( \frac{XY}{ZY} = \frac{WY}{VY} \)) and included angle equal (vertical angles), so triangles are similar by SAS Similarity.

Answer:

C) The triangles are similar by SAS Similarity.