Question

problem 6
in this figure, segment bc is parallel to segment de
how do you know that triangle abc is similar to triangle ade?

Explanation:

When two lines are parallel, corresponding angles are equal. Since $BC\parallel DE$, $\angle ABC=\angle ADE$ (corresponding angles) and $\angle ACB = \angle AED$ (corresponding angles), and $\angle BAC=\angle DAE$ (common - angle). By the AA (angle - angle) similarity criterion, two triangles are similar if two pairs of corresponding angles are equal.

Answer:

The two triangles $\triangle ABC$ and $\triangle ADE$ are similar by the AA (angle - angle) similarity criterion because $\angle ABC=\angle ADE$, $\angle ACB=\angle AED$ due to $BC\parallel DE$, and $\angle BAC=\angle DAE$ (common angle).