Question

Identify the correct explanation for why △ABC

and △DEC
are similar, and find EC
.

The figure shows two triangles A B C and D E C with common vertex C. Sides A B and E D are parallel. The length of segment A C is 18 units. The length of segment B C is 24 units. The length of segment D C is 24 units.

What is ec's value and how can I know?

Answer 1

C

As show.

Because AB//ED, so <B=<e, <A=<D

and <ABC=<ECB {to triangle with tree equal angles are alike}

and AC/CD=BC/EC

so 18/24=24/EC EC=24 times 24/18=32

Answer 2

△ABC and △DEC are similar because they both have the same angle at vertex C, and corresponding sides are proportional. To find EC, we use the similarity ratio of the two triangles, which is equal to the ratio of the lengths of corresponding sides. In this case, the ratio of AC to EC is 18/24, so EC = (24 x 18)/24 = 18 units.