Question

Identify the similar triangles (write a similarity statement), find x, and the

measure of the indicated side.

Answer 1

Problem 1:

x = 7

AB = 10

BC = 6

Explanation:

∡E = ∡D due to Alternate-Interior Angles

∡A = ∡C due to Alternate-Interior Angles

m∡B = m∡B

therefore, ΔABE ≈ ΔCBD

so AB = BC and we can use the following proportion to find 'x':

(x+3) / (2x-8) = 5/3

cross-multiply:

5(2x-8) = 3(x+3)

10x-40 = 3x+9

7x = 49

x = 7

AB = 7+3, or 10

BC = 2(7)-8, or 6

3 = x-8

11 = x

AB = 11+3, or 14

BC = 2(11)-8, or 14