7-6 Congruence Warm Up Problem of the Day Lesson Presentation Course 3

7-6 Congruence Warm Up Find the measure of the indicated angle. Course 3 7-6 Congruence Warm Up Find the measure of the indicated angle. 1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75° 55° 2. the third angle of a right triangle with an angle of 60° 30° 3. the supplement of a 35° angle 145°

7-6 Congruence Problem of the Day Course 3 7-6 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°

Course 3 7-6 Congruence M8G1.d: How do I use the properties of congruent figures to solve problems?

Course 3 7-6 Congruence Vocabulary correspondence

Course 3 7-6 Congruence A correspondence is a way of matching up two sets of objects. If 2 polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices (each vertex) in the 2nd polygon are written in order of correspondence with the 1st polygon.

7-6 Congruence Helpful Hint Course 3 7-6 Congruence Marks on the sides of a figure can be used to show congruence. AB @ QR (2 marks) BC @ PR (3 marks) AC = PQ (1 mark) Helpful Hint __

Example 1A: Writing Congruent Statements Course 3 7-6 Congruence Example 1A: Writing Congruent Statements Write a congruence statement for each pair of polygons. 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. 65 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.

Example 1B: Writing Congruent Statements Course 3 7-6 Congruence Example 1B: Writing Congruent Statements Write a congruence statement for each pair of polygons. 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. G @ P, so G corresponds to P. H @ Q, so H corresponds to Q. *The congruence statement is pentagon DEFGH @ pentagon MNOPQ.

7-6 Congruence Check It Out: Example 1A Course 3 7-6 Congruence Check It Out: Example 1A Write a congruence statement for each pair of polygons. 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 B | 60° 60° || |||| 120° 120° D ||| C A @ S, so A corresponds to S. Q R ||| 120° 120° B @ T, so B corresponds to T. || |||| C @ Q, so C corresponds to Q. 60° 60° | D @ R, so D corresponds to R. T S *The congruence statement is trapezoid ABCD @ trapezoid STQR.

7-6 Congruence Check It Out: Example 1B Course 3 7-6 Congruence Check It Out: Example 1B Write a congruence statement for each pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. 110° A B A @ M, so A corresponds to M. 110° B @ N, so B corresponds to N. F 140° 140° C 110° C @ O, so C corresponds to O. 110° E D D @ P, so D corresponds to P. N 110° O E @ Q, so E corresponds to Q. M 110° 140° F @ L, so F corresponds to L. 140° 110° P L *The congruence statement is hexagon ABCDEF @ hexagon MNOPQL. 110° Q

Example 2A: Using Congruence Relationships to Find Unknown Values Course 3 7-6 Congruence Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find a. a + 8 = 24 WX @ KL a = 16 –8 –8 Subtract 8 from both sides.

Example 2B: Using Congruence Relationships to Find Unknown Values Course 3 7-6 Congruence Example 2B: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find b. 6b = 30 ML @ YX 6 6 6b = 30 Divide both sides by 6. b = 5

Example 2C: Using Congruence Relationships to Find Unknown Values Course 3 7-6 Congruence Example 2C: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY @ quadrilateral JKLM. Find c. 5c = 85  J @  V 5 5 5c = 85 Divide both sides by 5. c = 17

7-6 Congruence Check It Out: Example 2A Course 3 7-6 Congruence Check It Out: Example 2A In the figure, quadrilateral JIHK @ quadrilateral QRST. Find a. 3a = 6 IH @ RS 3a = 6 3 3 Divide both sides by 3. 3a I H a = 2 6 4b° R S 120° J 30° Q K c + 10° T

7-6 Congruence Check It Out: Example 2B Course 3 7-6 Congruence Check It Out: Example 2B In the figure, quadrilateral JIHK @ quadrilateral QRST. Find b. 4b = 120  H @  S 4 4 4b = 120 Divide both sides by 4. 3a I H b = 30° 6 4b° R S 120° J 30° Q K c + 10° T

7-6 Congruence Check It Out: Example 2C Course 3 7-6 Congruence Check It Out: Example 2C In the figure, quadrilateral JIHK @ quadrilateral QRST. Find c. c + 10 = 30  K @  T –10 –10 c + 10 = 30 Subtract 10 from both sides. 3a I H c = 20° 90° 6 4b° R S 90° 120° J 30° Q c + 10° K T

7-6 Congruence Lesson Quiz In the figure, WXYZ @ ABCD 1. Find XY. 10 Course 3 7-6 Congruence Lesson Quiz In the figure, WXYZ @ ABCD 1. Find XY. 10 2. Find mB. 80° 3. Find CD. 8 4. Find mZ. 90°