Question

HELP DUE IN 15 MINS! In ΔABC, AB = 6 in, BC = 11 in, AC = 9 in. In ΔXYZ, XZ = 38.5 in, XY = 31.5 in, and YZ = 21 in.

1. . Are the two triangles similar?


Answer choices for number 1Yes, the sides are all proportional or No, the sides are not proportional.??


2. What is the Scale Factor=??

Answer 1

Let's verify is the corresponding sides have same ratio:

• ΔABC, sides: 6, 9, 11
• ΔXYZ, sides: 21, 31.5, 38.5

Ratios:

• 6/21 = 2/7 (divide by 3)
• 9/31.5 = 2/ 7 (divide by 4.5)
• 11/38.5 = 2/7 (divide by 5.5)

The ratios are same, so the triangles are similar

• Yes, the sides are all proportional

The scale factor (ΔABC to ΔXYZ) is 2/7 (or ΔXYZ to ΔABC is 7/2 = 3.5)