a Can you identify two pairs of congruent angles in the two triangles?
B
b Equate the ratios of two pairs of corresponding sides.
A
a Similar
Flowchart: See solution.
B
b x=10
Practice makes perfect
a Let's first label the vertices of the two triangles.
To prove that the triangles are similar, we have to show that at least two pairs of angles in the triangles are congruent. Examining the diagram, we can immediately identify a pair of vertical angles. By the Vertical Angles Theorem, we know that these are congruent.
Next, consider AE as a transversal to AB and DE. Now, we can also identify a pair of alternative interior angles because, if AB∥ DE, we know that ∠ A≅ ∠ E.
Since the triangles have two pairs of congruent angles, we can claim that they are similar by the AA Similarity condition.
Flowchart
Let's show this as a flowchart.
b From Part A, we established that the two triangles are similar. In similar triangles, the ratio of corresponding sides is always equal. Therefore, by identifying corresponding sides in our triangles, we can write an equation that involves x.
