Survey

Survey

Document related concepts

no text concepts found

Transcript

9-9 Congruent Figures California Standards Extension of MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Holt CA Course 1 9-9 Congruent Figures Vocabulary Side-Side-Side Rule Holt CA Course 1 9-9 Congruent Figures Look at the two patterns. 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. Holt CA Course 1 9-9 Congruent Figures Teacher Example 1A: Identifying Congruent Figures in the Real World Identify any congruent figures. A. The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure. Holt CA Course 1 9-9 Congruent Figures Teacher Example 1B: Identifying Congruent Figures in the Real World Identify any congruent figures. B. Holt CA Course 1 The sectors in the figure are congruent. 9-9 Congruent Figures Remember! Two figures are congruent if they have the same shape and size. Holt CA Course 1 9-9 Congruent Figures Student Practice 1A: Identify any congruent figures. A. The sides of the figures are are not congruent. Holt CA Course 1 9-9 Congruent Figures Student Practice 1B: Identify any congruent figures. B. The figures are not congruent. The figure on the outside is larger than the one on the inside. Holt CA Course 1 9-9 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. Holt CA Course 1 9-9 Congruent Figures Teacher Example 2: Identifying Congruent Triangles Determine whether the triangles are congruent. AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm 4 cm B 4 cm C 6 cm A Q 5 cm R 4 cm P 4 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. Holt CA Course 1 9-9 Congruent Figures Student Practice 2: Determine whether the triangles are congruent. AC = 8 m DF = 8 m AB = 6 m DE = 6 m BC = 10 m EF = 10 m B 6m E 10 m 10 m 6m A8 m C F 8 m D 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. Reading Math The notation ABC is read “triangle ABC.” Holt CA Course 1 9-9 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. Holt CA Course 1 9-9 Congruent Figures Teacher Example 3: Using Congruence to Find Missing Measures Determine the missing measure in the set of congruent polygons. A. The corresponding angles of congruent polygons are congruent. The missing angle measure is 110°. Holt CA Course 1 9-9 Congruent Figures Teacher Example 3: Using Congruence to Find Missing Measures Determine the missing measure in the set of congruent polygons. B. The corresponding sides of congruent polygons are congruent. The missing side length is 28 mm. Holt CA Course 1 9-9 Congruent Figures Student Practice 3A: Determine the missing measure in the set of congruent polygons. A. ? 120° 135° The corresponding sides are congruent. The missing side length is 4 ft. 6 ft 45° 60° 8 ft 8 ft 45° 5 ft Holt CA Course 1 5 ft 60° 6 ft 135°120° 4 ft 9-9 Congruent Figures Student Practice 3B: Determine the missing measure in the set of congruent polygons. B. The corresponding angles are congruent. The missing angle measure is 130°. 5 ft 6 ft 130° 110° 120° 4 ft 100° Holt CA Course 1 80° 10 ft 10 ft 100° 4 ft 80° 120° 8 ft 110° ? 5 ft 6 ft 8 ft 9-9 Congruent Figures Lesson Quiz 1. Identify any congruent figures. none 2. Determine the missing measures in the set of congruent polygons. a = 11, b = 6, c = 110° Holt CA Course 1

Related documents