Cogito
Integrated Math 1 · Chapter 6 · Lesson 3
Triangle Congruence Criteria
How little you need to check.
12 problems · about 21 minutes · G-CO.B.8
What this lesson teaches
The student applies SSS, SAS, ASA and AAS to establish triangle congruence.
- SSS, SAS, ASA and AAS each prove triangle congruence.
- SSA is ambiguous and AAA gives only similarity.
- Three well-chosen parts fix a triangle completely.
Warm Up
Straightforward practice. Get the method working first.
5 problemsThree pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer 1
Why SSS.
Why does SSA fail to prove congruence?
Answer Two different triangles can satisfy the same measurements.
Why The measurements do not pin down one triangle.
Two angles and the side between them. 1 SSS, 2 SAS, 3 ASA.
Answer 3
Why Angle, side, angle.
Two sides and the included angle. 1, 2 or 3?
Answer 2
Why Side, angle, side.
Does AAA prove congruence? 1 yes, 0 no.
Answer 0
Why Same shape, any size.
Build It Up
The same ideas with more to keep track of.
3 problemsHow many parts does a triangle have in total, sides and angles?
Answer 6
Why Three of each.
How many matching parts are needed for congruence?
Answer 3
Why Three, well chosen.
Angles 50 and 60 are given. What is the third, in degrees?
Answer 70
Why 180 − 110.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each combination by whether it proves congruence.
Answer Proves congruence: SSS, ASA · Does not: SSA, AAA
Why One is ambiguous and one gives only similarity.
Two angles and a non-included side. Does it prove congruence? 1 yes, 0 no.
Answer 1
Why The third angle follows, so it is AAS.
The Criterion: Three pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer 1
Why SSS.
The Failure: Two sides and a non-included angle. Does this prove congruence? 1 yes, 0 no.
Answer 0
Why No, SSA is ambiguous.