1. Proving Triangles Congruent

2. If we can show all 3 pairs of corr. sides are congruent, the triangles
SSS
If we can show all 3 pairs of corr.
sides are congruent, the triangles
have to be congruent.

3. SAS Show 2 pairs of sides and the included angles are congruent and
the triangles have to be congruent.
Non-included
angles
Included
angle

4. This is called a common side. It is a side for both triangles.
We’ll use the reflexive property.

5. SSS SAS SAS Common side Vertical angles Parallel lines alt int angles

6. ASA, AAS and HL A ASA – 2 angles and the included side S A
AAS – 2 angles and
The non-included side A A S

7. HL ( hypotenuse leg ) is used
only with right triangles, BUT,
not all right triangles.
ASA HL

8. SOME REASONS WE’LL BE USING
DEF OF MIDPOINT
DEF OF A BISECTOR
VERT ANGLES ARE CONGRUENT
DEF OF PERPENDICULAR BISECTOR
REFLEXIVE PROPERTY (COMMON SIDE)
PARALLEL LINES ….. ALT INT ANGLES

9. Proof 1) O is the midpoint of MQ and NP 2) 3) 4) 1) Given
Given: O is the midpoint of MQ and NP
Prove:
1) O is the midpoint of MQ and NP 2) 3) 4)
1) Given
2) Def of midpoint
3) Vertical Angles
4) SAS

10. AAS C Given: CX bisects ACB A ˜ B Prove: ∆ACX ˜ ∆BCX = 1 2 = A X B P A
CX bisects ACB Given
1 = Def of angle bisc
A = B Given
CX = CX Reflexive Prop
∆ACX ˜ ∆BCX AAS =

11. Proof
Given:
Prove: 1) 2) 3)
1) Given
2) Reflexive Property
3) SSS

12. Proof 1) 2) 3) 4) 1) Given 2) Alt. Int. <‘s Thm
Prove: 1) 2) 3) 4)
1) Given
2) Alt. Int. <‘s Thm
3) Reflexive Property
4) SAS