Recall the definition of similar triangles. How can you use the angle measures to check if triangles are similar?
Yes, see solution.
Practice makes perfect
We want to decide whether the two given triangles are similar. Let's take a look at the given figure. We can mark the measures of the unknown angles as a, b, c, and d.
If two angles in a triangle are congruent to two angles in another triangle, then the third angles are also congruent and the triangles are similar. We will use this fact to check if the two given triangles are similar. First, let's recall the definition of alternate interior angles.
Alternate Interior Angles
Angles that lie between the pair of lines on opposite sides of the transversal.
We can see that the 40^(∘) angle and angle c are alternate interior angles. Because the bases of the two triangles are parallel, we know that these angles are congruent and have the same measure. Let's mark it on our figure.
Next, notice that the 68^(∘) angle and angle b are vertical angles. We know that vertical angles are congruent, so the measure of the angle b is 68^(∘).
We found that two angles in the lower triangle are congruent to two angles in the upper triangle. Because of this, angles a and d must also be congruent and the given triangles are similar.
