Check if the corresponding sides that include the congruent angles are proportional.
Are the triangles similar? Yes. Similarity statement: △ ABC~△ FBD Explanation: See solution.
Practice makes perfect
Since we are given two sides lengths of △ ABC and △ FBD, as well as the measure of the angle included between them, we will check if the corresponding sides of these triangles are proportional to determine if they are similar.
Let's evaluate the ratios between the corresponding sides. We will start with the shorter sides.
DB/CB=6/10= 0.6
Now, we will evaluate the ratio between the longer sides. Remember that, according to the Segment Addition Postulate, the length of AB is the sum of lengths of AF and FB.
FB/AB=9/6+ 9= 9/15= 0.6
As we can see, the ratio between corresponding sides is the same for each pair. This means that the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of a second triangle, and the included angles are congruent. Therefore, by the Side-Angle-Side Similarity Theorem, △ ABC and △ FBD are similar.
