1. Congruence
Lesson 9-5

2. Congruence In chapter 6 we learned about similar figures.
Similar figures have the same shape but not the same size.
Congruent figures are exactly the same in shape and size.
The symbol ~ means congruent. A X
corresponding angles
corresponding sides B C Z Y
ABC ~ XYZ

3. Congruent Figures Congruent sides are noted by the slash marks on theX
corresponding angles 15
45°
45°
corresponding sides
45° B C Y
45° Z
ABC ~ XYZ
Congruent sides are noted by the slash marks on the
Corresponding line segments.

4. Congruent Figures
It’s easier to see the corresponding sides and angles when the figures
are in matching positions. So sometimes you need to turn or flip one
of the figures in order to find their corresponding sides or angles.
corresponding angles A
45°
45°
corresponding sides
45° B
45° C

5. Congruence
Just as slash marks on the line segments indicate equal sides, arcs on the angles indicate equal angles.

6. Congruence
There are three ways to identify whether triangles are congruent:
If all three sides are equal (SSS)
If all three sides are equal, then all the angles are
Equal as well, therefore the triangles are congruent.

7. Congruence
A second way is if 2 sides and the angle in between are equal then all sides and angles are equal and therefore congruent.
Side-Angle-Side (SAS)

8. Congruence
And the third way is if 2 angles and the side in between are the same, then the triangles are congruent. Angle-Side-Angle (ASA)

9. Try This Name the sides of the triangles that are congruent. A X B C YZ

10. Try This Name the sides of the triangles that are congruent. AB and XY
AC and XZ and
BC and YZ A X B C Y Z

11. Try This Name the angles of the triangles that are congruent. A X B CZ

12. Try This Name the angles of the triangles that are congruent.X
Angle A and X,
Angle B and Y and
Angle C and Z B C Y Z

13. Try This
Give the reason that the following are congruent (example: SSS, SAS, ASA)

14. Try This
Give the reason that the following are congruent (example: SSS, SAS, ASA)
SAS