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

NameDate

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

Bo's school garden is a right-triangle lawn with a square flower bed planned on each side. What is the area of the bed on the hypotenuse, in square feet?
Kira draws a right triangle on poster paper and a square on each side. What is the area of the square on the hypotenuse, in square cm?
Milo marks a right-triangle sunflower patch with a square bed on each side. The sunflowers will be taller than everyone. What is the area of the bed on the hypotenuse, in square feet?
Ren's math book shows a right triangle with a square on each leg. How long is the hypotenuse, in inches?
5.
Ari's park map shows three straight paths that make a right triangle. The legs are the two sides that make the right angle. Which two sides are the legs?
- the red and green sides
- the red and blue sides
- the blue and green sides
6.
Bo flies a kite. The string, the ground and a straight line down from the kite make a right triangle. Which two sides are the legs?
- the red and blue sides
- the blue and green sides
- the red and green sides
7.
A tree, its shadow and a sun ray from the treetop make a right triangle in Esme's sketch. The legs are the two sides that make the right angle. Which two sides are the legs?
- the red and green sides
- the red and blue sides
- the blue and green sides
8.
Jun's math book shows a right triangle standing on its longest side. Which equation is true for the squares on its sides?
- 40² + 41² = 9²
- 9² + 41² = 40²
- 9² + 40² = 41²
9.
Kira draws a right triangle and labels its sides with a sharp pencil. Which equation is true for the squares on its sides?
- 28² + 53² = 45²
- 28² + 45² = 53²
- 45² + 53² = 28²
10.
Milo's book shows a right triangle turned on its side. Which equation is true for the squares on its sides?
- 33² + 65² = 56²
- 56² + 65² = 33²
- 33² + 56² = 65²

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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