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

4. 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 triangle QRP.

5. 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 trapezoid STQR.

6. 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 hexagon MNOPQL.

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

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

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

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

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

12. In the figure, quadrilateral JIHK @ quadrilateral QRST.
Try This!
In the figure, quadrilateral 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. 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….

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

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
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)
Q12
Congruent Triangles Worksheet #1