Check if the corresponding sides that include the congruent angles are proportional.
Are the triangles similar? Yes. Similarity statement: △ ABE ~ △ ADC Explanation: See solution.
Practice makes perfect
We are given two side lengths of △ ABE and △ ADC, and we know that the included angle between these sides is congruent as ∠ A≅∠ A by the Reflexive Property. Therefore, to determine if the triangles are similar, we will check if the corresponding sides of these triangles are proportional.
Let's evaluate the ratios between the corresponding sides. We will start with the shorter sides. Remember that, according to the Segment Addition Postulate, the length of AD is the sum of lengths of AE and ED.
AB/AD=5/7+3=5/10=0.5
Next, we will evaluate the ratio between the longer sides.
AE/AC=7/5+ 9=7/14=0.5
As we can see, the ratio between corresponding sides is the same for each pair, so the lengths of the corresponding sides are proportional. Therefore, by the Side-Angle-Side Similarity Theorem, △ ABE and △ ADC are similar triangles.
