Question

In the diagram shown overline AD and intersect at point E. overline AB and overline CD are parallel . Given the segment length shown in the picture, which of the following is the length overline AE

1) 11.25
2) 10.8
3) 10
4) 7.5

Answer 1

11.25

Explanation:

Since AB and CD are parallel, ∠D is congruent to ∠A and ∠C is congruent to ∠B. Therefore the two triangles are similar by the AA postulate. Now, the corresponding sides are in proportion

Since AE ↔ DE and AB ↔ CD

So, AE/CD = AB/CD

AE/5 = 9/4

AE = 9(5)/4

= 45/4 = 11.25