Question

In triangle ABC, segment DE is parallel to segment AC. Find CB if CE = 6, AC = 20, and DE = 15.

A) 8
B) 10
C) 12
D) 14

Answer 1

To find CB, use the property that corresponding angles formed by parallel lines are equal. Set up a proportion and solve for BC. The length of CB is 30 units.

Step-by-step explanation:

To find CB, we can use the property that corresponding angles formed by parallel lines are equal. Since DE is parallel to AC, we can conclude that angle CED is equal to angle CEA.

Since triangle CED is similar to triangle CBA by AA similarity, we can set up a proportion:

CD/BC = CE/AC

CD/BC = 6/20

CD/BC = 3/10

CD = (3/10) * BC

Using the fact that CD + DE = CE, we have (3/10) * BC + 15 = 6

(3/10) * BC = 6 - 15

(3/10) * BC = -9

BC = -9 * (10/3)

BC = -30

Therefore, the length of CB is 30 units.