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7-6

7-6. Congruence. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 7-6. Congruence. Course 3. Warm Up Find the measure of the indicated angle. 1 . the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°. 55°.

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7-6

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  1. 7-6 Congruence Warm Up Problem of the Day Lesson Presentation Course 3

  2. 7-6 Congruence Course 3 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°

  3. 7-6 Congruence Course 3 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°

  4. 7-6 Congruence Course 3 M8G1.d: How do I use the properties of congruent figures to solve problems?

  5. 7-6 Congruence Course 3 Vocabulary correspondence

  6. 7-6 Congruence Course 3 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. 7-6 Congruence Helpful Hint 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) __ __ __ __ __ __ Course 3

  8. 7-6 Congruence 65 65 Course 3 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. 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.

  9. 7-6 Congruence Course 3 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.

  10. 7-6 Congruence Course 3 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.

  11. 7-6 Congruence Course 3 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° 140° 140° F B@N, so B corresponds to N. C 110° C@O, so C corresponds to O. E 110° D N D@P, so D corresponds to P. 110° O M E@Q, so E corresponds to Q. 140° 110° 110° F@L, so F corresponds to L. P 140° L *The congruence statement is hexagon ABCDEF@ hexagon MNOPQL. 110° Q

  12. 7-6 Congruence WX @ KL a + 8 = 24 –8 –8 a = 16 Course 3 Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. Find a. Subtract 8 from both sides.

  13. 7-6 Congruence ML @ YX 6b = 30 6b = 30 6 6 Course 3 Example 2B: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. Find b. Divide both sides by 6. b = 5

  14. 7-6 Congruence  J @ V 5c = 85 5c = 85 5 5 Course 3 Example 2C: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. Find c. Divide both sides by 5. c = 17

  15. 7-6 Congruence IH @ RS 3a = 6 3a = 6 3 3 Course 3 Check It Out: Example 2A In the figure, quadrilateral JIHK@ quadrilateral QRST. Find a. Divide both sides by 3. 3a I H a = 2 6 4b° S R 120° J 30° Q K c + 10° T

  16. 7-6 Congruence  H @ S 4b = 120 4b = 120 4 4 Course 3 Check It Out: Example 2B In the figure, quadrilateral JIHK@ quadrilateral QRST. Find b. Divide both sides by 4. 3a I H b = 30° 6 4b° S R 120° J 30° Q K c + 10° T

  17. 7-6 Congruence  K @ T c + 10 = 30 c + 10 = 30 –10 –10 Course 3 Check It Out: Example 2C In the figure, quadrilateral JIHK@ quadrilateral QRST. Find c. Subtract 10 from both sides. 3a I H c = 20° 6 90° 4b° S R 120° 90° J 30° c + 10° Q K T

  18. 7-6 Congruence 1. Find XY. 3. Find CD. Course 3 Lesson Quiz In the figure, WXYZ@ABCD 10 80° 2. Find mB. 8 90° 4. Find mZ.

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