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Cogito

Integrated Math 1 · Chapter 6 · Lesson 3

Practice Worksheet

Triangle Congruence Criteria

How little you need to check.

12 problems · about 21 minutes · G-CO.B.8

NameDate

Figure — use these to answer the problems

Fix two legs and the right angle between them. Exactly one triangle results, which is SAS.
adjacent = 4opposite = 3hyp = 5
One leg4
Other leg3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Three pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.

    Answer

  2. Why does SSA fail to prove congruence?

    • Two different triangles can satisfy the same measurements.
    • It gives only two pieces of information.

  3. Two angles and the side between them. 1 SSS, 2 SAS, 3 ASA.

    Answer

  4. Two sides and the included angle. 1, 2 or 3?

    Answer

  5. Does AAA prove congruence? 1 yes, 0 no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many parts does a triangle have in total, sides and angles?

    Answer

  2. How many matching parts are needed for congruence?

    Answer

  3. Angles 50 and 60 are given. What is the third, in degrees?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each combination by whether it proves congruence.

    Write each item under the heading it belongs to: SSS · ASA · SSA · AAA

    Proves congruence

    Does not

  2. Two angles and a non-included side. Does it prove congruence? 1 yes, 0 no.

    Answer

  3. The Criterion

    Three pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.

    Answer

  4. The Failure

    Two sides and a non-included angle. Does this prove congruence? 1 yes, 0 no.

    Answer