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McGraw Hill Glencoe Algebra 2, 2012 View details

7. Congruent and Similar Figures

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Exercise 1 Page P21

Two figures are congruent if all of their sides and angles are congruent. Two figures are similar if all the angles are congruent and the ratio between corresponding sides is the same for all pairs of corresponding sides.

Similar.

Practice makes perfect

We want to determine whether the figures are similar, congruent, or neither.

For two figures to be congruent, two conditions must be satisfied.

All sides are congruent.
All angles are congruent.

For our exercise, the sides do not have the same lengths. Therefore, the figures are not congruent. To be similar figures, two conditions must be satisfied.

All corresponding angles must be congruent.
The ratio between corresponding sides must be the same for all pairs of corresponding sides.

All of the corresponding angles are congruent, so let's see if the second condition is also satisfied.

Corresponding Side Lengths	Ratio	Simplified Ratio
10 and 5	10:5	2:1
7 and 3.5	7:3.5	2:1
9 and 4.5	9:4.5	2:1

Since all of the ratios can be simplified to 2:1, the second condition is also satisfied. Therefore, the figures are similar.

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Exercises p.21-P21

Exercise 1 Page P21

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