Cogito
Grade 8 Math · Chapter 9 · Lesson 1
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
What this lesson teaches
The child applies the Pythagorean theorem to find a missing side of a right triangle.
- In a right triangle, a² + b² = c².
- c is the hypotenuse, opposite the right angle.
- It works only for right triangles.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Placing an Irrational Number: √40 lies between which two whole numbers? Give the smaller.
Answer 6
Why Between 6 and 7.
Review — Cube Roots: Cube root of 216?
Answer 6
Why 6.
Warm Up
Straightforward practice. Get the method working first.
4 problemsLegs 9 and 12. Hypotenuse?
Answer 15
Why 15.
Which side is c in a² + b² = c²?
Answer The longest side, opposite the right angle.
Why c is the hypotenuse.
Legs 5 and 12. Hypotenuse?
Answer 13
Why 25 + 144 = 169.
Legs 8 and 15. Hypotenuse?
Answer 17
Why 64 + 225 = 289.
Build It Up
The same ideas with more to keep track of.
2 problemsHypotenuse 10, one leg 6. Other leg?
Answer 8
Why 100 − 36 = 64.
Does the theorem work for any triangle?
Answer No. Right triangles only.
Why Check for the right angle.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Ladder: A right triangle has legs 3 and 4. What is the hypotenuse?
Answer 5
Why 5.
The Missing Leg: A right triangle has hypotenuse 13 and one leg 5. What is the other leg?
Answer 12
Why 12.