Question

date:
period
similar triangle measures practice

1. the triangles are similar. solve for x.
2. the triangles are similar. solve for x and y.

△abc∼△def. solve for x and y.

1. △jkl∼△mno. solve for x and y.
2. △pqr has been dilated by a scale factor of 1.76 to form △pqr. find x and y.
3. △def has been dilated by a scale factor of 1/2 to form △def. find x and y.

ij∼△pqr. solve for x, y, and z.

1. △abc∼△def. solve for x, y, and z.

Explanation:

Step1: Identify Similar Triangles Property

For similar triangles, corresponding sides are proportional, and corresponding angles are equal. Let's solve problem 1 first. The first triangle has sides 8 and 12, the second has sides \( x \) and 9. So the ratio of corresponding sides should be equal. So \(\frac{8}{x}=\frac{12}{9}\) (or \(\frac{12}{8}=\frac{9}{x}\), depending on correspondence). Let's assume the sides 12 and 9 are corresponding, 8 and \( x \) are corresponding. So cross - multiply: \( 12x = 8\times9 \).

Step2: Solve for \( x \)

Calculate \( 8\times9 = 72 \). Then \( 12x=72 \), divide both sides by 12: \( x=\frac{72}{12}=6 \).

Answer:

For problem 1, \( x = 6 \)