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Cogito

Grade 8 Math · Chapter 1 · Lesson 2

Practice Worksheet

Congruence

Same shape, same size, wherever it sits.

10 problems · about 18 minutes · 8.G.A.2

NameDate

Figure — use these to answer the problems

A flip carries the shape onto its mirror image. Both are congruent.
Not used by a flip1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Moving a Shape Without Changing It”

    (2, 9) reflected across the vertical axis. New first coordinate?

    Answer

  2. From “Moving a Shape Without Changing It”

    What does a rigid motion preserve?

    • Lengths and angles.
    • The position on the grid.

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Congruent shapes, one side is 15. The matching side?

    Answer

  2. How is congruence defined?

    • One can be carried onto the other by rigid motions.
    • They look the same.

  3. Congruent shapes, one side is 12. The matching side?

    Answer

  4. Congruent shapes, one angle is 90. The matching angle?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Can a reflection be part of proving congruence?

    • Yes.
    • No.

  2. Does a dilation preserve congruence?

    • No. It changes lengths.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Matching Side

    Two congruent triangles. One has a side of 7. What is the matching side on the other?

    Answer

  2. The Matching Angle

    Two congruent shapes. One has an angle of 55 degrees. What is the matching angle?

    Answerdegrees