Grade 8 · Math

8th grade Why a² + b² = c²: squares on the sides worksheet

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Why a² + b² = c²: squares on the sides

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Kira glues a paper square onto each side of a right triangle for an art project. What is the area of the big square on the hypotenuse, in square inches?
Bo sews a right-triangle quilt patch with a square patch on each side. The cat already wants to nap on it. What is the area of the big square patch, in square inches?
Jun lays a square of tiles on each side of a right triangle. What is the area of the big square of tiles, in square inches?
Luz draws a right triangle on a poster with crayons, then a square on each side. What is the area of the big square on the hypotenuse, in square cm?
Milo's drawing robot draws a right triangle with a square on each side, then beeps proudly. How long is the hypotenuse, in cm?
Pia's math book shows a right triangle with squares on its legs. How long is the hypotenuse, in cm?
Ren's garden club plans square beds beside a right-triangle path. How long is the hypotenuse, in feet?
8.
Tala looks at the side of a wheelchair ramp. It is a right triangle. The hypotenuse is the side across from the right angle. Which side is the hypotenuse?
- the green side
- the blue side, the longest one
- the red side
9.
Zee cuts a square sandwich from corner to corner and turns one half over. The hypotenuse is the side across from the right angle. Which side is the hypotenuse?
- the red side
- the green side
- the blue side
10.
Esme folds a square of paper corner to corner and holds the triangle point down. The hypotenuse is the side across from the right angle. Which side is the hypotenuse?
- the green side
- the blue side
- the red side

8th grade Why a² + b² = c²: squares on the sides worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Why a² + b² = c²: squares on the sides. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can point to the legs (the two sides at the right-angle mark) and the hypotenuse (the side across from it), however the triangle is turned.
I can show that the squares on the legs together have the same area as the square on the hypotenuse, and use it: 256 + 900 = 1156.
I can explain why with a tilted square on grid paper, and check a² + b² = c² for a measured triangle.

Standard: 8.G.B.6 (the theorem)

Words to know

right angle: A square corner. Drawings mark it with a small square.

leg: One of the two sides that meet at the right-angle mark.

hypotenuse: The side across from the right angle. It is always the longest side.

square on a side: A square drawn outward with that side as one of its edges.

area: How much flat space a shape covers, in square units.

a² + b² = c²: The square on leg a plus the square on leg b equals the square on hypotenuse c.

Common mistakes

Your child found the length of the long side when the question asked for the area of the square on it.

Your child took the smaller square away from the bigger one, when the square on the longest side holds both small squares together.

Your child added the areas of the two small squares but gave that area as the length of the long side. The area is the big square; its side is the number that times itself makes that area.

What to say

Ask: is the answer a length, like 25 cm, or an area, like 625 square cm?

Ask: should the square on the longest side be bigger than both small squares, or smaller?

Ask: which number times itself makes it?

Questions parents ask

What is the most common mistake with why a² + b² = c²: squares on the sides?

Your child found the length of the long side when the question asked for the area of the square on it.

How can I help my child with why a² + b² = c²: squares on the sides?

Ask: is the answer a length, like 25 cm, or an area, like 625 square cm?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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