Question

Suppose that CA = 12, CB = 20, DF = 6, and FE = 10. Which additional fact would guarantee that the triangles are SIMILAR? A) AB = 24 and DE = 12 B) AB = 30 and DE = 18 C) AB = 12 and DE = 24 Eliminate D) m∠A = m∠D

Answer 1

A) AB = 24 and DE = 12

Explanation:

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar. Then:

`(CA)/(DF)=(12)/(6)=2`

On the other hand:

`(CB)/(FE)=(20)/(10)=2`

So, the additional fact that would guarantee that the the triangles are similar is AB=24 and DE=12 given that:

`(AB)/(DE)=(24)/(12)=2`

So the three pairs of sides have the same ration, in consequence, the angles are also equal.

Answer 2

A) AB = 24 and DE = 12

Explanation:

Since the side CA is the double of side DF and the side CB is double the side FE, to get SIMILAR triangles, we also need the third sides to in the same proportion... so AB = 24 and DE = 12

So the first triangle would have measurements:

CA = 12

CB = 20

AB = 24

The second triangle would be scaled by 2:

DF = 6

FE = 10

DE = 12