1. CONGRUENT
TRIANGLES
Sections 4-2, 4-3, 4-5
Jim Smith JCHS

2. When we talk about congruent triangles,
we mean everything about them Is congruent.
All 3 pairs of corresponding angles are equal….
And all 3 pairs of corresponding sides are equal

3. For us to prove that 2 people are identical twins, we don’t need to show that all “2000” body parts are equal. We can take a short cut and show 3 or 4 things are equal such as their face, age and height. If these are the same I think we can agree they are twins. The same
is true for triangles. We don’t need to prove all 6 corresponding parts are
congruent. We have 5 short cuts or methods.

4. 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.

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

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

7. Which method can be used to prove the triangles are congruent

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

9. PART 2

10. 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

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

12. When Starting A Proof, Make The Marks On The Diagram Indicating
The Congruent Parts. Use The Given
Info, Properties, Definitions, Etc.
We’ll Call Any Given Info That Does Not Specifically State Congruency
Or Equality A PREREQUISITE

13. 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

14. SAS Our Outline P rerequisites S ides A ngles Triangles ˜ A C = B 1 2
Given: AB = BD
EB = BC
Prove: ∆ABE ˜ ∆DBC A C = B 1 2
Our Outline
P rerequisites
S ides
A ngles
Triangles ˜
SAS E D =

15. A C B = SAS E D P S A ∆’s none AB = BD Given 1 = 2 Vertical angles
Given: AB = BD
EB = BC
Prove: ∆ABE ˜ ∆DBC B 1 2 =
SAS E D
STATEMENTS REASONS P S A
∆’s
none
AB = BD Given
1 = Vertical angles
EB = BC Given
∆ABE ˜ ∆DBC SAS =

16. 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 =

17. Can you prove these triangles
are congruent?