1. G.6 Proving Triangles Congruent Visit www.worldofteaching.com
For 100’s of free powerpoints.

2. Objective: Students will be able to determine triangle congruence
Objective: Students will be able to determine triangle congruence. EQ: What strategies do you use when determining triangle congruence?

3. The Idea of Congruence
Two geometric figures with exactly the same size and shape. A C B D E F

4. Do you need all six ?
NO !
SSS
SAS
ASA
AAS

5. The triangles are congruent by SSS.
Side-Side-Side (SSS)
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. B A C
Side E
Side F D
Side
AB  DE
BC  EF
AC  DF
ABC   DEF
The triangles are congruent by SSS.

6. Side-Angle-Side (SAS) The triangles are congruent by SAS.
If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.
included
angle B E
Side F A C
Side D
AB  DE
A   D
AC  DF
Angle
ABC   DEF
The triangles are congruent by SAS.

7. Angle-Side-Angle (ASA) The triangles are congruent by ASA.
If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent.
included
side B E
Angle
Side F A C D
Angle
A   D
AB  DE
 B   E
ABC   DEF
The triangles are congruent by ASA.

8. Angle-Angle-Side (AAS) The triangles are congruent by AAS.
If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent.
Non-included
side B A C
Angle E D F
Side
Angle
A   D
 B   E
BC  EF
ABC   DEF
The triangles are congruent by AAS.

9. Name That Postulate
(when possible)
SAS
ASA
SSA
AAS
Not enough info!

10. Reflexive Sides and Angles
Vertical Angles,
Reflexive Sides and Angles
When two triangles touch, there may be additional congruent parts.
Vertical Angles
Reflexive Side
side shared by two
triangles

11. Name That Postulate SAS SAS SSA AAS Vertical Angles Reflexive Property
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
Vertical Angles
Reflexive Property
SSA
AAS
Not enough info!

12. Reflexive Sides and Angles
When two triangles overlap, there may be additional congruent parts.
Reflexive Side
side shared by two
triangles
Reflexive Angle
angle shared by two

13. Let’s Practice B  D AC  FE A  F
Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
B  D
For SAS:
AC  FE
A  F
For AAS: