Chapter 7.5, Problem 2WE

To determine

To find: Two similar triangles.

Answer to Problem 2WE

$\Delta ABC$ and $\Delta THJ$

Explanation of Solution

Given information:

Calculation:

In $\Delta ABC$ ,

  $\begin{array}{l}\angle A=40°\\ \angle B=80°\\ \angle C=180°-(40°+80°)=60°\end{array}$

In $\Delta THJ$ ,

  $\begin{array}{l}\angle H=80°\\ \angle J=60°\\ \angle T=180°-(80°+60°)=40°\end{array}$

From $\Delta ABC$ and $\Delta THJ$ ,

  $\begin{array}{l}\angle A=\angle T\\ \angle B=\angle H\\ \angle C=\angle J\end{array}$

AA Similarity Postulate states that, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Thus, $\Delta ABC$ and $\Delta THJ$ are similar triangles.