Unit 1 Chapter 2 Lesson 2 Congruence Pg. 107

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.

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) Helpful Hint __

Writing Congruent Statements Write a congruence statement for each pair of polygons. 55 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.

Write a congruence statement for each pair of polygons. 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.

Write a congruence statement for each pair of polygons. 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° F 140° 140° C 110° 110° E D 110° N O M 140° 110° P 110° 140° L Q 110° The congruence statement is hexagon ABCDEF @ hexagon MNOPQL.

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.

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

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

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

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

In the figure, quadrilateral JIHK @ quadrilateral QRST. 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

Congruent Triangles

NOT THE OTHER TWO…. SSS ASA SAS AAS 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………. SSS ASA SAS AAS NOT THE OTHER TWO….

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

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

Determine whether the triangles are congruent 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

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

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