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Cogito

Geometry · Chapter 3 · Lesson 1

Practice Worksheet

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

NameDate

Figure — use these to answer the problems

Fixing two legs of a right triangle fixes everything else about it.
adjacent = 4opposite = 3hyp = 536.87°
  • sin — opposite over hypotenuse0.60
  • cos — adjacent over hypotenuse0.80
  • tan — opposite over adjacent0.75
  • The marked angle36.87°
One leg4
Other leg3
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Dilations and Scale Factor”

    Area 4, factor 3. New area?

    Answer

  2. From “Transformations on Coordinates”

    (7, 2) reflected across the x-axis. New y?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Congruent triangles, one angle is 68°. The matching angle?

    Answer

  2. Why is SSA not a criterion?

    • Two different triangles can fit the same data.
    • It is hard to use.

  3. Two sides and the angle between them. Which criterion?

    • SAS.
    • SSA.

  4. Two angles and the side between them. Which criterion?

    • ASA.
    • AAS.

Build It Up

The same ideas with more to keep track of.

2 problems

  1. How many pairs of equal parts do the criteria need?

    Answer

  2. Congruent triangles, one side is 13. The matching side?

    Answer

Stretch Yourself

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

2 problems

  1. The Criterion

    Three pairs of equal sides. Which criterion is that?

    • SSS.
    • SAS.

  2. The One That Fails

    Is SSA a valid congruence criterion?

    • No. It can give two different triangles.
    • Yes.