Question

explain why the triangles are similar. then find the distance represented by x.
why are the triangles similar? choose the correct answer below.
a. the corresponding sides of two triangles are proportional, so the triangles are similar by the sss - theorem.
b. there is a pair of congruent angles and the sides that include the two vertical angles are also congruent, so the triangles are similar by the sas - theorem.
c. there is a pair of congruent angles and the sides that include the two vertical angles are proportional, so the triangles are similar by the sas - theorem.
d. there is a pair of congruent angles and a pair of congruent right angles, so the triangles are similar by the aa - postulate.
e. there is a pair of congruent angles and the sides that include the two vertical angles are proportional, so the triangles are similar by the aa - postulate.
x = (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Identify similar - triangle reason

There is a pair of congruent angles (vertical angles) and a pair of congruent right - angles, so the triangles are similar by the AA - Postulate. The correct answer for why the triangles are similar is D.

Step2: Set up proportion

Since the triangles are similar, the ratios of their corresponding sides are equal. We have the proportion $\frac{x}{28}=\frac{6}{8}$.

Step3: Solve for x

Cross - multiply: $8x = 28\times6$. Then $8x=168$. Divide both sides by 8: $x=\frac{168}{8}=21$.

Answer:

21