8-5 Congruent Figures Learn to identify congruent figures and to use congruence to solve problems.

8-5 Congruent Figures Which center circle do you think is bigger? In spite of appearances, the two center circles are congruent. Their apparent differences are optical illusions. One way to determine whether figures are congruent is to see if one figure will fit exactly over the other one. Look at the two patterns.

8-5 Congruent Figures Identify any congruent figures. Additional Example 1A: Identifying Congruent Figures in the Real World The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.

8-5 Congruent Figures Identify any congruent figures. Additional Example 1B: Identifying Congruent Figures in the Real World The sectors in the figure are congruent.

8-5 Congruent Figures Identify any congruent figures. Check It Out: Example 1A The sides of the figures are are not congruent.

8-5 Congruent Figures Identify any congruent figures. Check It Out: Example 1B The figures are not congruent. The figure on the outside is larger than the one on the inside.

8-5 Congruent Figures If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles, if the corresponding sides are congruent, then the corresponding angles will always be congruent. This is called the Side-Side-Side Rule. Because of this rule, when determining whether triangles are congruent, you only need to determine whether the sides are congruent.

8-5 Congruent Figures Determine whether the triangles are congruent. Additional Example 2: Identifying Congruent Triangles 4 cm 6 cm 5 cm 4 cm A B C R P Q AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent.

8-5 Congruent Figures Determine whether the triangles are congruent. Check It Out: Example 2 AC = 8 m AB = 6 m BC = 10 m DF = 8 m DE = 6 m EF = 10 m The notation ABC is read “triangle ABC.” Reading Math A B C F D E 6 m 8 m 10 m By the Side-Side-Side Rule, ABC is congruent to DEF, or ABC  DEF. If you flip one triangle, it will fit exactly over the other.

8-5 Congruent Figures For polygons with more than three sides, it is not enough to compare the measures of their sides. For example, the corresponding sides of the figures below are congruent, but the figures are not congruent. If you know that two figures are congruent, you can find the missing measures in the figures.

8-5 Congruent Figures Determine the unknown measure in the set of congruent polygons. Additional Example 3: Using Congruence to Find Unknown Measures The unknown angle measure is 110°. The corresponding parts of congruent polygons are congruent. The unknown side length is 28 mm.

8-5 Congruent Figures Check It Out: Example 3A Determine the unknown measure in the set of congruent polygons. 6 ft 8 ft 5 ft 120° 135° 60° 45° 6 ft 8 ft 5 ft 4 ft 120° 135° 45° 60° The unknown side length is 4 ft. The corresponding sides are congruent. ?

8-5 Congruent Figures Check It Out: Example 3B Determine the unknown measure in the set of congruent polygons. The unknown angle measure is 130°. The corresponding angles are congruent. 6 ft 8 ft 4 ft 5 ft 4 ft 8 ft 10 ft 120° 130° 110° 100° 80° 110° 80° 100° 120° ?

8-5 Congruent Figures Lesson Quiz 1. Identify any congruent figures. 2. Determine the unknown measures in the set of congruent polygons. none a = 11, b = 6, c = 110°