McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Similar Triangles
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Exercise 15 Page 566

What can you say about the corresponding sides of the given triangles?

Yes, see solution.

Practice makes perfect

Let's begin with recalling that, according to the Vertical Angles Theorem, vertical angles are always congruent. In our exercise this means that ∠ ABE is congruent to ∠ CBD.

We are given that the distances from the pupil to the top and bottom of the object is congruent, and the distances from the pupil to the top and bottom of the image on the retina is congruent. AB=EB and CB=DB

This means that the ratio of the corresponding sides will be constant. AB/CB=EB/DB The lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle, and the included angles are congruent. Therefore, by the Side-Angle-Side Similarity Theorem, these triangles are similar.