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Cogito

Grade 8 Math · Chapter 9 · Lesson 1

Practice Worksheet

The Pythagorean Theorem

The two smaller squares add to the biggest.

10 problems · about 19 minutes · 8.G.B.6, 8.G.B.7, 8.G.B.8

NameDate

Figure — use these to answer the problems

The squares on the sides are what the theorem is about.

Area · squares inside

12

Perimeter · walk around

14

3 × 4 = 12 · 3 + 4 + 3 + 4 = 14

Side3
Side4
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Placing an Irrational Number”

    √40 lies between which two whole numbers? Give the smaller.

    Answer

  2. From “Cube Roots”

    Cube root of 216?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Legs 9 and 12. Hypotenuse?

    Answer

  2. Which side is c in a² + b² = c²?

    • The longest side, opposite the right angle.
    • Any of the three.

  3. Legs 5 and 12. Hypotenuse?

    Answer

  4. Legs 8 and 15. Hypotenuse?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Hypotenuse 10, one leg 6. Other leg?

    Answer

  2. Does the theorem work for any triangle?

    • No. Right triangles only.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Ladder

    A right triangle has legs 3 and 4. What is the hypotenuse?

    Answer

  2. The Missing Leg

    A right triangle has hypotenuse 13 and one leg 5. What is the other leg?

    Answer