1. 7-6
Congruence
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. 7-6 Congruence Warm Up Find the measure of the indicated angle.
Course 3
7-6
Congruence
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. 7-6 Congruence Problem of the Day
Course 3
7-6
Congruence
Problem of the Day
The measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle?
mABC = 38°; mCBD = 52°

4. Course 3
7-6
Congruence
M8G1.d:
How do I use the properties of congruent figures to solve problems?

5. Course 3
7-6
Congruence
Vocabulary
correspondence

6. Course 3
7-6
Congruence
A correspondence is a way of matching up two sets of objects.
If 2 polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices (each vertex) in the 2nd polygon are written in order of correspondence with the 1st polygon.

7. 7-6 Congruence Helpful Hint
Course 3
7-6
Congruence
Marks on the sides of a figure can be used to show congruence.
QR (2 marks)
PR (3 marks)
AC = PQ (1 mark)
Helpful Hint __

8. Example 1A: Writing Congruent Statements
Course 3
7-6
Congruence
Example 1A: 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. 65
Q, so A corresponds to Q.
R, so B corresponds to R.
P, so C corresponds to P.
*The congruence statement is triangle triangle QRP.

9. Example 1B: Writing Congruent Statements
Course 3
7-6
Congruence
Example 1B: Writing Congruent Statements
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.
M, so D corresponds to M.
N, so E corresponds to N.
O, so F corresponds to O.
P, so G corresponds to P.
Q, so H corresponds to Q.
*The congruence statement is pentagon pentagon MNOPQ.

10. 7-6 Congruence Check It Out: Example 1A
Course 3
7-6
Congruence
Check It Out: Example 1A
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
S, so A corresponds to S. Q R
|||
120°
120°
T, so B corresponds to T. ||
||||
Q, so C corresponds to Q.
60°
60° |
R, so D corresponds to R. T S
*The congruence statement is trapezoid trapezoid STQR.

11. 7-6 Congruence Check It Out: Example 1B
Course 3
7-6
Congruence
Check It Out: Example 1B
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.
110° A B
M, so A corresponds to M.
110°
N, so B corresponds to N. F
140°
140° C
110°
O, so C corresponds to O.
110° E D
P, so D corresponds to P. N
110° O
Q, so E corresponds to Q. M
110°
140°
L, so F corresponds to L.
140°
110° P L
*The congruence statement is hexagon hexagon MNOPQL.
110° Q

12. Example 2A: Using Congruence Relationships to Find Unknown Values
Course 3
7-6
Congruence
Example 2A: 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.

13. Example 2B: Using Congruence Relationships to Find Unknown Values
Course 3
7-6
Congruence
Example 2B: 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

14. Example 2C: Using Congruence Relationships to Find Unknown Values
Course 3
7-6
Congruence
Example 2C: 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

15. 7-6 Congruence Check It Out: Example 2A
Course 3
7-6
Congruence
Check It Out: Example 2A
In the figure, quadrilateral quadrilateral QRST.
Find a.
3a = 6 RS
3a = 6
Divide both sides by 3. 3a I H
a = 2 6
4b° R S
120° J
30° Q K
c + 10° T

16. 7-6 Congruence Check It Out: Example 2B
Course 3
7-6
Congruence
Check It Out: Example 2B
In the figure, quadrilateral quadrilateral QRST.
Find b.
4b = 120
  S
4b = 120
Divide both sides by 4. 3a I H
b = 30° 6
4b° R S
120° J
30° Q K
c + 10° T

17. 7-6 Congruence Check It Out: Example 2C
Course 3
7-6
Congruence
Check It Out: Example 2C
In the figure, quadrilateral quadrilateral QRST.
Find c.
c + 10 = 30
  T
–10 –10
c + 10 = 30
Subtract 10 from both sides. 3a I H
c = 20°
90° 6
4b° R S
90°
120° J
30° Q
c + 10° K T

18. 7-6 Congruence Lesson Quiz In the figure, WXYZ @ ABCD 1. Find XY. 10
Course 3
7-6
Congruence
Lesson Quiz
In the figure, ABCD
1. Find XY. 10
2. Find mB.
80°
3. Find CD. 8
4. Find mZ.
90°