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Glencoe Math: Course 3, Volume 2

GM

Glencoe Math: Course 3, Volume 2 View details

5. Similar Triangles and Indirect Measurement

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Exercise 21 Page 560

If two polygons are similar, then their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

Yes, see solution.

Practice makes perfect

Polygons that have the same shape are called similar polygons. If two polygons are similar, then their corresponding angles are congruent and the lengths of their corresponding sides are proportional. With this information in mind, let's examine the given figures.

Two rectangles are described: a small one with a length of 5 units and a width of 4 units, and a large one with a length of 10 units and a width of 8 units.

We can see that all of the angles in both figures are right angles. Therefore, all of the corresponding angles are congruent. Note that the given figures are rectangles. Therefore their opposite sides are congruent.

given figures

Let's now check whether corresponding sides are proportional.

Proportion	Simplify
4/8	1/2
5/10	1/2
4/8	1/2
5/10	1/2

Since all of the proportions are the same, all of the corresponding sides are proportional. Therefore, the polygons are similar.

Subchapter links

Guided Practice p.556

Independent Practice p.557

H.O.T. Problems p.558

Standardized Test Practice p.558-560

Extra Practice p.559

Common Core Review p.560