Cogito
Geometry · Chapter 3 · Lesson 1
Triangle Congruence Criteria
How little you need to know to be sure.
10 problems · about 21 minutes · G-CO.B.7, G-CO.B.8, G-SRT.B.5
What this lesson teaches
The student applies SSS, SAS, ASA, AAS, and HL to prove triangles congruent.
- SSS, SAS, ASA, AAS, and HL prove triangles congruent.
- SSA does not, because two triangles can fit.
- Congruence then makes every corresponding part equal.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Dilations and Scale Factor: Area 4, factor 3. New area?
Answer 36
Why 36.
Review — Transformations on Coordinates: (7, 2) reflected across the x-axis. New y?
Answer -2
Why −2.
Warm Up
Straightforward practice. Get the method working first.
4 problemsCongruent triangles, one angle is 68°. The matching angle?
Answer 68
Why 68°.
Why is SSA not a criterion?
Answer Two different triangles can fit the same data.
Why It does not determine the triangle.
Two sides and the angle between them. Which criterion?
Answer SAS.
Why Included angle.
Two angles and the side between them. Which criterion?
Answer ASA.
Why Included side.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many pairs of equal parts do the criteria need?
Answer 3
Why Three of the right kind.
Congruent triangles, one side is 13. The matching side?
Answer 13
Why Corresponding parts are equal.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Criterion: Three pairs of equal sides. Which criterion is that?
Answer SSS.
Why SSS.
The One That Fails: Is SSA a valid congruence criterion?
Answer No. It can give two different triangles.
Why SSA is not a criterion.