1. Modules 5 & 6 Triangle Congruence Proofs

2. Lesson 5.2 – ASA Triangle Congruence Theorem
ASA Practice
Included Side – a side that is in between two angles when discussing triangle congruency statements.

3. Lesson 5.3 – SAS Triangle Congruence Theorem
SAS Practice
Included Angle – an angle that is in between two sides when discussing triangle congruency statements.

4. Lesson 5.4 – SSS Triangle Congruence Theorem
SSS Practice

5. Lesson 6.2 – AAS Triangle Congruence Theorem
Non-Included Side – a side that is not in between two angles when discussing triangle congruency statements.
AAS Practice

6. NON-CONGRUENCE – AAA and SSA
AAA does NOT guarantee congruence – Two triangles can have the same angle measures but not be the same size.
These triangles are NOT the congruent since they are not the same size. Is there anything about these triangles other than their angles that is the same?
Answer – THEIR SHAPE IS THE SAME!

7. NON-CONGRUENCE – SSA (don’t write this backwards ever!!)
But why does SSA not prove congruence?

8. NON-CONGRUENCE – SSA (don’t write this backwards ever!!)
But why does SSA not prove congruence?

9. Lesson 6.3 – HL Triangle Congruence Theorem
This is actually a special case of SSA that works!

10. Lesson 6.3 – HL Triangle Congruence Theorem
Take our triangle from our SSA exploration:

11. Lesson 6.3 – HL Triangle Congruence Theorem
Take our triangle from our SSA exploration:

12. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

13. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

14. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

15. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

16. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

17. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:

18. Lesson 6.3 – HL Triangle Congruence Theorem
Imagine if we keep shortening the red leg of the triangle:
When the leg gets as short as possible, what angle do we have here?
A right angle!
So this is a right triangle!
HL Practice