Question

for #23-24, use the figure below.

1. identify the similar triangles in the figure.
2. find the value of ( x ), showing all of your work.

chapter 4
12 glencoe geometry

Explanation:

Step1: Identify similar triangles

Triangles $\triangle ABD$ and $\triangle ECD$ are similar (right triangles, shared angle $\angle D$, AA similarity).

Step2: Set up proportion

Corresponding sides are proportional:
$\frac{AB}{EC} = \frac{BD}{CD}$
Substitute values: $\frac{x}{3} = \frac{6+4}{4}$

Step3: Simplify and solve for x

Simplify denominator: $\frac{x}{3} = \frac{10}{4}$
Cross-multiply: $4x = 3 \times 10$
Calculate: $4x = 30$
Solve for x: $x = \frac{30}{4} = \frac{15}{2}$

Answer:

1. $\triangle ABD \sim \triangle ECD$
2. $x = \frac{15}{2}$ or $7.5$