Introduces the 5 conditions for congruent triangles

2. Triangle Style

3. WHAT IS CONGRUENCY?
When two shapes are exactly the same size and shape we say they are
CONGRUENT
WHICH OF THESE SHAPES IS CONGRUENT WITH THE FIRST SHAPE?

4. Too small
Too big
Even though their direction changed, they are
the same size and shape.

5. WHICH OF THE FOLLOWING ARE CONGRUENT?

6. WHICH OF THE FOLLOWING ARE CONGRUENT?

7. THERE ARE 5 CONDITIONS WE CAN USE TO
DETERMINE IF 2 TRIANGLES ARE CONGRUENT
•
•
•
•
•
SSS -- Side-Side-Side
SAS – Side-Angle-Side
ASA – Angle-Side-Angle
AAS – Angle-Angle-Side
RHS – Right-Hypotenuse-Side

8. WHY DO THEY WORK?
These rules work because they show us the MINIMUM information we need to
know to be able to use Geometry to determine the remaining angles and side
lengths. Therefore, if we memorize these rules, we can know immediately if
triangles are congruent or not.

9. SIDE – SIDE – SIDE
Just like for the images, if all the sides of a triangle are the same, then that must
mean that the triangles are congruent.
This is known as the Side-Side-Side condition or SSS

10. SIDE – ANGLE – SIDE
If you know two sides and a single angle, we can determine the final leg length
and angles, therefore we know these angles must be congruent.
This is known as the Side-Angle-Side condition or SAS

11. ANGLE – SIDE – ANGLE
If we know two angles and a side we can use geometry to determine the other
angles and sides, therefore we can determine that the triangles have the same
angles and side lengths. Therefore we only need to know 2 angles and 1 side
to determine that the triangles are congruent.
This is known as the Angle-Side-Angle condition or ASA

12. ANGLE – ANGLE – SIDE
If we know two angles and a side we can use geometry to determine the other
angles and sides, therefore we can determine that the triangles have the same
angles and side lengths. Therefore we only need to know 2 angles and 1 side to
determine that the triangles are congruent.
This is known as the Angle-Angle-Side condition or AAS

13. RIGHT – HYPOTENUSE – SIDE
If we know one angle is a right angle, and we know the hypotenuse and a
side, we can determine the rest of the angles and sides using geometry.
Therefore we only need to know that there is a right angle and the lengths of
the hypotenuse and one side to determine the triangles are congruent.
This is known as the Right Hypotenuse Side condition RHS

14. RULES THAT
DON’T WORK

15. ANGLE – ANGLE – ANGLE
If all angles are the same that does not mean they are congruent. The
leg lengths could be different.

16. SIDE – SIDE – ANGLE
Even if we know two sides and an angle, we do not have enough information to
determine the rest of the triangle’s features.

17. PRACTICE – ARE THESE CONGRUENT?
IF SO BY WHICH CONDITION?

18. PRACTICE – ARE THESE CONGRUENT?
IF SO BY WHICH CONDITION?
YES-ASA

20. NO- AAA IS NOT A CONDITION FOR
CONGRUENCY.

22. NO –SSA IS NOT
A CONDITION
FOR
CONGRUENCY

24. YESSSS

26. YES - SAS

28. YESAAS

30. YES – RHS