To solve for \( x \) using the AA (Angle-Angle) Similarity Postulate, we know that the triangles are similar, meaning their corresponding sides are proportional.
Given:
1. One pair of corresponding sides is \( 7.5 \) and \( 15 \).
2. Another pair of corresponding sides is \( 18 \) and \( x \).
Let's set up the proportion:
\[
\frac{7.5}{15} = \frac{18}{x}
\]
First, simplify \( \frac{7.5}{15} \):
\[
\frac{7.5}{15} = \frac{1}{2}
\]
So the proportion can be rewritten as:
\[
\frac{1}{2} = \frac{18}{x}
\]
Next, solve for \( x \) by cross-multiplying:
\[
1 \cdot x = 2 \cdot 18
\]
\[
x = 36
\]
Thus, the value of \( x \) is \( 36 \).
The triangles are similar by the AA Similarity Postulate. Find the value of x.
7.5 15 18 x
27
1.2
12
270
1 answer