8-9 Congruent Figures Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Find the measure of the third angle in the triangle, given two angle measures °, 104° 2. 32°, 63° 3. 90°, 38° 4. 42°, 88° 18° 85° 50° Course Congruent Figures 52°

Problem of the Day Draw triangles ABC and DEF so that a. AB = DE and BC = EF b. angle A is congruent to angle D. c. the triangles are not congruent. Course Congruent Figures DE F AB C

Learn to identify congruent figures and to use congruence to solve problems. Course Congruent Figures

Vocabulary Side-Side-Side Rule Insert Lesson Title Here Course Congruent Figures

Course 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.

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

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

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

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

Course Congruent Figures If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles in particular, the corresponding angles will always be congruent if the corresponding sides are 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.

Determine whether the triangles are congruent. Additional Example 2: Identifying Congruent Triangles Course Congruent Figures 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.

Determine whether the triangles are congruent. Check It Out: Example 2 Course Congruent Figures 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.

Course 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.

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

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

Check It Out: Example 3B Determine the missing measure in the set of congruent polygons. Insert Lesson Title Here Course Congruent Figures The missing 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° ?

Lesson Quiz 1. Identify any congruent figures. Insert Lesson Title Here Course Congruent Figures 2. Determine the missing measures in the set of congruent polygons. none a =11, b =6, c = 110°