Pre-Algebra

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

2. 5-6 Congruence Pre-Algebra 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.

3. 5-6 Congruence 55 55 Pre-Algebra Example 1A: Writing Congruent Statements Write a congruence statement for the 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.

4. 5-6 Congruence Pre-Algebra Example 1B: Writing Congruent Statements Write a congruence statement for the 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.

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

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

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

8. 5-6 Congruence Pre-Algebra 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.

9. 5-6 Congruence Pre-Algebra Try This: Example 1A Write a congruence statement for the 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.

10. 5-6 Congruence Pre-Algebra Try This: Example 1B Write a congruence statement for the 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

11. 3a = 6 IH ≅ RS 3a = 6 5-6 Congruence 3 3 Pre-Algebra Try This: Example 2A 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

12. 4b = 120 ∠H ≅∠S 4b = 120 5-6 Congruence 4 4 Pre-Algebra Try This: Example 2B 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

13. –10 –10 c + 10 = 30 ∠K ≅∠T c + 10 = 30 5-6 Congruence Pre-Algebra Try This: Example 2C 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