Pre-Algebra 5-6 Congruence 5-6 Congruence Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 5-6 Congruence Warm Up Find the measure of the indicated angle. Pre-Algebra 5-6 Congruence 1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75° 2. the third angle of a right triangle with an angle of 60° 3. the supplement of a 35° angle 55° 30° 145°

Pre-Algebra 5-6 Congruence Problem of the Day The measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle? mABC = 38°; mCBD = 52°

Pre-Algebra 5-6 Congruence Learn to use properties of congruent figures to solve problems.

Pre-Algebra 5-6 Congruence correspondence Vocabulary

Pre-Algebra 5-6 Congruence A correspondence is a way of matching up two sets of objects. If two polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices in the second polygon are written in order of correspondence with the first polygon.

Pre-Algebra 5-6 Congruence Additional Example 1A: Writing Congruent Statements The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence. A  Q, so A corresponds to Q. B  R, so B corresponds to R. C  P, so C corresponds to P. The congruence statement is triangle ABC  triangle QRP. Write a congruence statement for the pair of polygons. 55

Pre-Algebra 5-6 Congruence Additional Example 1B: Writing Congruent Statements The vertices in the first pentagon are written in order around the pentagon starting at any vertex. D  M, so D corresponds to M. E  N, so E corresponds to N. F  O, so F corresponds to O. The congruence statement is pentagon DEFGH  pentagon MNOPQ. G  P, so G corresponds to P. H  Q, so H corresponds to Q. Write a congruence statement for the pair of polygons.

Pre-Algebra 5-6 Congruence Try This: Example 1A The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence. A  S, so A corresponds to S. B  T, so B corresponds to T. C  Q, so C corresponds to Q. The congruence statement is trapezoid ABCD  trapezoid STQR. A B C D Q R ST D  R, so D corresponds to R. | || ||| |||| | || ||| |||| Write a congruence statement for the pair of polygons. 60° 120° 60° 120°

Pre-Algebra 5-6 Congruence Try This: Example 1B The vertices in the first pentagon are written in order around the pentagon starting at any vertex. A  M, so A corresponds to M. B  N, so B corresponds to N. C  O, so C corresponds to O. The congruence statement is hexagon ABCDEF  hexagon MNOPQL. D  P, so D corresponds to P. E  Q, so E corresponds to Q. A B C D E F N O P Q L M F  L, so F corresponds to L. Write a congruence statement for the pair of polygons. 140° 110° 140° 110°

Pre-Algebra 5-6 Congruence Additional Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY  quadrilateral JKLM. a = 16 –8 –8 Subtract 8 from both sides. A. Find a. a + 8 = 24 WX  KL

Pre-Algebra 5-6 Congruence In the figure, quadrilateral VWXY  quadrilateral JKLM b = 30 Divide both sides by 6. B. Find b. 6b = 30 ML  YX b = 5 Additional Example 2B: Using Congruence Relationships to Find Unknown Values

Pre-Algebra 5-6 Congruence 5c = 85 J  V 5 5 5c = 85 Divide both sides by 5. C. Find c. c = 17 In the figure, quadrilateral VWXY  quadrilateral JKLM. Additional Example 2C: Using Congruence Relationships to Find Unknown Values

Pre-Algebra 5-6 Congruence Try This: Example 2A In the figure, quadrilateral JIHK  quadrilateral QRST. A. Find a. 3a3a 4b° 6 30° Q 120° R S H I J K 3a = a = 2 c + 10° T 3a = 6 IH  RS Divide both sides by 3.

Pre-Algebra 5-6 Congruence B. Find b. Divide both sides by b = 120 b = 30° 4b = 120 H  S Try This: Example 2B In the figure, quadrilateral JIHK  quadrilateral QRST. 3a3a 4b° 6 30° Q 120° R S H I J K c + 10° T

Pre-Algebra 5-6 Congruence C. Find c. c = 20° Subtract 10 from both sides. –10 c + 10 = 30 K  T Try This: Example 2C 3a3a 4b° 6 30° 90° Q 120° 90° R S H I J K T c + 10° In the figure, quadrilateral JIHK  quadrilateral QRST.

Pre-Algebra 5-6 Congruence Lesson Quiz In the figure, WXYZ  ABCD 2. Find mB. 4. Find mZ ° 8 90° 1. Find XY. 3. Find CD.