Question

question 7
find the measure of zy if the following figures are similar.
(there are two triangles: one red with vertices a, b, c where ac is 6 cm, ab is 2 cm; one green with vertices x, z, y where xz is 3 cm.)

Explanation:

Step1: Identify Similar Triangles

The two triangles are similar, so their corresponding sides are proportional. Let the length of \( ZY \) be \( x \). The red triangle has sides \( AC = 6 \, \text{cm} \) and \( AB = 2 \, \text{cm} \). The green triangle has sides \( XZ = 3 \, \text{cm} \) and \( ZY = x \).

Step2: Set Up Proportion

For similar triangles, \( \frac{AC}{XZ} = \frac{AB}{ZY} \). Substituting values: \( \frac{6}{3} = \frac{2}{x} \).

Step3: Solve for \( x \)

Simplify \( \frac{6}{3} = 2 \), so \( 2 = \frac{2}{x} \). Cross - multiply: \( 2x = 2 \). Divide both sides by 2: \( x = 1 \).

Answer:

The measure of \( ZY \) is \( 1 \, \text{cm} \).