Question

Complete the explanation of how you know whether the triangles are similar. If possible, find AD rounded to the nearest tenth. A 5.0 B 9.0 C 20.0 D E Because two pairs of angles are congruent, the triangles are similar by the (select) AD=

Answer 1

In triangles ABC and ADE,

BC is parallel to DE

Since all the angles in triangle ABC are equianguar with the angles in triangle ADE,

Then, triangle ABC is similar to triangle ADE

to find AD:

ratio of corresponding sides is given by

$\begin{gathered} \frac{BC}{DE}\text{ =}\frac{AB}{AD} \\ \\ \frac{9}{20}\text{ = }\frac{5}{AD} \\ 9AD\text{ = 5 }\times\text{ 20} \\ 9AD=100 \\ AD=\frac{100}{9} \\ AD\text{ = 11.11} \\ AD\cong\text{ 11.1 ( nearest tenth)} \end{gathered}$