Question

Explain why the triangles are similar and then findthe length of AB.AABAB9DB15

Answer 1

AB=10

1) Considering that similar triangles, have congruent angles and proportional sides, and considering that the line segment ED, is parallel to the line segment BC

2) Then we can state that

m∠AED ≅ m∠ACB because they are corresponding angles.

Having said that, we found the measure of AB, by writing a proportion between the sides of the smaller triangle and the larger one. So AD (smaller one) = 6 and its corresponding AB (Larger one) = 6 +x.

And ED (smaller) over BC (larger)

`\begin{gathered} (AD)/(AB)=(ED)/(BC) \\ (6)/(6+x)=(9)/(15) \\ 9(6+x)=15*6 \\ 54+9x\text{ =}90 \\ 9x=90-54 \\ 9x=36 \\ x=4 \end{gathered}`

3) Hence, the side AB, is

AB = 6 +x

AB = 6+4

AB=10