Unit 1 Chapter 2 Lesson 2

1. Unit 1 Chapter 2 Lesson 2 Congruence Pg. 107

2. Learn to use properties of congruent figures to solve problems. Vocabulary correspondence 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.

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

4. 55 55 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. The congruence statement is triangle ABC@ triangle QRP.

5. Try this! 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 Q R ||| 120° 120° || |||| 60° 60° | T S The congruence statement is trapezoid ABCD@ trapezoid STQR.

6. Try this! Write a congruence statement for each pair of polygons. 110° A B The vertices in the first pentagon are written in order around the pentagon starting at any vertex. 110° 140° F C 140° 110° 110° E D 110° N O 140° M 110° P 110° 140° L Q 110° The congruence statement is hexagon ABCDEF@ hexagon MNOPQL.

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

8. ML @ YX 6b = 30 6b = 30 6 6 Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. Find b. Divide both sides by 6. b = 5

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

10. Try This! In the figure, quadrilateral JIHK@ quadrilateral QRST. Find a. 3a I H 6 4b° S R 120° J 30° Q c + 10° K T

11. Try This! In the figure, quadrilateral JIHK@ quadrilateral QRST. Find b. 3a I H 6 4b° S R 120° J 30° Q K c + 10° T

12. Try This! In the figure, quadrilateral JIHK@ quadrilateral QRST. Find c. 3a I H 6 S R 90° 4b° 90° 120° 30° J Q c + 10° K T

13. Congruent Triangles

14. We have learned about Congruent Polygons • Congruency Statements lead to corresponding angles and sides • Congruent simply means the same size and shape • We will now expand this to study Congruent Triangles • We will use four acronyms………. AAS ASA SSS SAS NOT THE OTHER TWO….

15. Congruent Triangles • If two figures are exactly the same size and shape, they are congruent. • Two triangles are congruent if the following corresponding parts of two triangles are congruent. • Three Sides (SSS) • Two angles and the included side (ASA) • Two sides and the included angle (SAS) • Two angles then a side (AAS) • Video below if to show why SSA and AAA do not work • http://www.youtube.com/watch?v=DWWwo4l_s9g&feature=player_embedded

16. Example • Determine whether the triangles are congruent. If so, write a congruence statement and tell why D B C A E

17. Determine whether the triangles are congruent. If so, write a congruence statement and tell why S P J K M L Q U T R 2 mm

18. Find the value of “x” in the following congruent triangle 60° (4x – 20)° 6 ft 2 yds

19. Homework • HC: pg.111-112 (1-5, 7-10) • CC: pg. 111-112 (1-5, 7, 8, 10) • www.ixl.com Q12 • Congruent Triangles Worksheet #1