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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 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°.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 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. California Standards MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures.

  4. Vocabulary correspondence congruent

  5. A correspondence is a way of matching up two sets of objects. Congruentfigures have the same shape and size. If two polygons are congruent, all of their corresponding sides and angles are congruent. To write a congruence statement, the vertices in the second polygon have to be written in order of correspondence with the first polygon.

  6. 55 55 Additional Example 1: Writing Congruent Statements A. Write a congruence statement for each pair of polygons. A corresponds to Q. A@Q B corresponds to R. B@R C corresponds to P.C@P The congruence statement is triangle ABC@ triangle QRP.

  7. Additional Example 1: Writing Congruent Statements B. 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 corresponds to M. D@M E corresponds to N. E@N F corresponds to O. F@O G corresponds to P. G@P H corresponds to Q. H@Q The congruence statement is pentagon DEFGH@ pentagon MNOPQ.

  8. Check It Out! Example 1 A. Write a congruence statement for each pair of polygons. A B | A corresponds to S. A@S 60° 60° || |||| B corresponds to T. B@T 120° 120° ||| D C C corresponds to Q. C@Q Q R D corresponds to R. D@R ||| 120° 120° || |||| The congruence statement is trapezoid ABCD@ trapezoid STQR. 60° 60° | T S

  9. Check It Out! Example 1 B. Write a congruence statement for each pair of polygons. A corresponds to M. A@M 110° A B B corresponds to N. B@N 110° C corresponds to O. C@O 140° 140° F C 110° D corresponds to P. D@P E 110° D N 110° E corresponds to Q. E@Q O M 140° 110° F corresponds to L. F@L 110° P 140° L The congruence statement is hexagon ABCDEF@ hexagon MNOPQL. 110° Q

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

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

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

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

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

  15. K @T c + 10 = 30 c + 10 = 30 –10 –10 Check It Out! Example 2 In the figure, quadrilateral JIHK@ quadrilateral QRST. C. 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

  16. 4. Find CD. Lesson Quiz 1. The figures above are congruent. Write a congruence statement. WXYZ @ ABCD 10 80° 3. Find mB. 2. Find XY. 8 90° 3. Find mZ.

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