1. Warm Up Triangle ADE is an isosceles triangle with the given measures.
Find the length of side DE. 2)

2. 8-5 Learn to use properties of congruent figures to solve problems.
Congruence
Learn to use properties of congruent figures to solve problems.

3. Course 3
8-5
Congruence
Vocabulary
correspondence

4. Course 3
8-5
Congruence
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.

5. 8-5 Congruence Helpful Hint
Course 3
8-5
Congruence
Marks on the sides of a figure can be used to show congruence.
QR (1 mark)
PR (2 mark)
PQ (3 mark)
Helpful Hint __

6. Additional Example 1A: Writing Congruent Statements
Course 3
8-5
Congruence
Additional 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. 55
A corresponds to  .
B corresponds to  .
C corresponds to  .
The congruence statement is triangle triangle QRP.

7. Additional Example 1B: Writing Congruent Statements
Course 3
8-5
Congruence
Additional 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.
D corresponds to  .
E corresponds to  .
F corresponds to  .
G corresponds to  .
H corresponds to  .
The congruence statement is pentagon pentagon MNOPQ.

8. 8-5 Congruence Check It Out: Example 1A
Course 3
8-5
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
A corresponds to  . Q R
|||
120°
120°
B corresponds to  . ||
||||
C corresponds to  .
60°
60° |
D corresponds to  . T S
The congruence statement is trapezoid trapezoid STQR.

9. 8-5 Congruence Check It Out: Example 1B
Course 3
8-5
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
A corresponds to  .
110°
B corresponds to  . F
140°
140° C
110°
C corresponds to  .
110° E D
D corresponds to  . N
110° O
E corresponds to  M
110°
140°
F corresponds to 
140°
110° P L
The congruence statement is hexagon hexagon MNOPQL.
110° Q

10. Course 3
8-5
Congruence
Additional Example 2A: Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral quadrilateral JKLM.
Find a.

11. Course 3
8-5
Congruence
Additional Example 2B: Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral quadrilateral JKLM.
Find b.

12. Course 3
8-5
Congruence
Additional Example 2C: Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral quadrilateral JKLM.
Find c.

13. 8-5 Congruence Check It Out: Example 2A
Course 3
8-5
Congruence
Check It Out: Example 2A
In the figure, quadrilateral quadrilateral QRST.
Find a. 3a I H 6
4b° R S
120° J
30° Q K
c + 10° T

14. 8-5 Congruence Check It Out: Example 2B
Course 3
8-5
Congruence
Check It Out: Example 2B
In the figure, quadrilateral quadrilateral QRST.
Find b. 3a I H 6
4b° R S
120° J
30° Q K
c + 10° T

15. 8-5 Congruence Check It Out: Example 2C
Course 3
8-5
Congruence
Check It Out: Example 2C
In the figure, quadrilateral quadrilateral QRST.
Find c. 3a I H
90° 6
4b° R S
90°
120° J
30° Q
c + 10° K T

16. Determine if the two figures are congruent
using transformations?
Explain the transformation.
Translation

17. Determine if the two figures are congruent
using transformations?
Explain the transformation.
Rotation by 90 followed by
translation
Rotation

18. Determine if the two figures are congruent
using transformations?
Explain the transformation.
Reflection across y-axis
followed by translation