1. Triangle Congruence
Section 4-6

2. Are these triangles congruent?
Yes, Angle-Side-Angle
Side
ASA (Unit 4-6) b
Angle a c a c
Angle b
Angle
Side

3. Angle-Side-Angle Congruence (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of another, then the triangles are congruent. B D A A C F F E

4. Given the parallelogram
Use ASA to explain why A B D C
It’s given that AB=CD (S) and DA=BC (S), and AC=CA (S) by symmetric property. So triangles = by SSS.
Angle
Alternate Interior Angles Theorem
Side
Reflexive Property of Congruence
Angle
Alternate Interior Angles Theorem

5. Can you use ASA to prove Explain.
NO; <KLN=<MNL by Alt Int <s Thm (A)
LN=NL by symmetric property (S)
But cannot determine if <KNL=<MLN (A)
Nope. We only have one angle and one side

6. Are these triangles congruent?
Yes, Angle-Angle-Side
Angle
AAS (Unit 4-6) b
Angle c
Side a a
Side c
Angle b
Angle

7. Angle-Angle-Side Congruence (AAS)
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another, then the triangles are congruent. B B D D
This is really just using ASA and Third Angle Theorem A A C F F E

8. Are these triangles congruent?
Yes, Angle-Angle-Side
Angle
Angle
AAS (Unit 4-6) b c
Side a a
Side c
Angle b
Angle
Third Angle Theorem tells us that these angles are congruent as well
So with that extra step we can also prove congruence by ASA

9. Can you use AAS to prove Explain.
YES; <B=<D by Alt Int <s Thm (A)
<BCA=<DCE by Vertical <s Thm (A)
It’s given that BC=DC (S)
Yes
Angle
Alternate Interior Angles Theorem
Angle
Vertical Angles Theorem
Side
Given
We can also choose to use ASA.

10. Can you use AAS to prove Explain.
YES; <B=<D by Alt Int <s Thm (A)
<BCA=<DCE by Vertical <s Thm (A)
It’s given that BC=DC (S)
Yes
Angle
Alternate Interior Angles Theorem
Side
Given
Angle
Alternate Interior Angles Theorem

11. Hypotenuse-Leg Congruence (HL)
In a right triangle, if the hypotenuse and leg of one triangle are congruent to the hypotenuse and leg of another, then the triangles are congruent. B D A C C F E E

12. Can you use HL to prove Explain.
NO; You are given a right triangle and can conclude that VY=VY (L) by the reflexive property, but you cannot determine if VX=VZ (H)

13. ? ? Are these triangles congruent?
No, Side-Side-Angle or Angle-Side-Side is not a method for proving triangle congruence
Note: we know for sure the length of b but not the measure of the angle between a and b ? ? a a b b b b c d