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 - Challenge Me

NameDate

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

Noah draws a right triangle on grid paper, legs 1 cm and 4 cm, then the square on its hypotenuse. That square comes out tilted. What is its area, in square cm?
Pia sketches a right triangle on grid paper with legs 2 cm and 5 cm. The square on its hypotenuse is tilted. What is that square's area, in square cm?
Ren's puzzle card shows a tilted square on the hypotenuse of a right triangle with legs 3 cm and 5 cm. What is the tilted square's area, in square cm?
Tala's robot draws a right triangle on grid paper, legs 2 cm and 7 cm, and a tilted square on its hypotenuse. What is that square's area, in square cm?
Zee measures a right-triangle corner of the school garden for square herb beds, one on each side. What is the area of the bed on the hypotenuse, in square meters?
Bo measures a right-triangle sunflower plot with a square bed on each side. What is the area of the bed on the hypotenuse, in square meters?
Not to scale. Jun has three paper squares that fit the sides of a right triangle. Two of them are labeled. What is the area of the unlabeled square, in square cm?
Luz's quilt has square patches on the three sides of a right-triangle patch. One label fell off. What is the area of the unlabeled patch, in square inches?
Milo's garden has square beds on the three sides of a right-triangle lawn. One sign is missing. What is the area of the unlabeled bed, in square feet?
10.
Pia labels the sides of a right triangle q, s and u in pencil. Which equation is true for the squares on its sides?
- q² + u² = s²
- s² + u² = q²
- q² + s² = u²
- q + s = u

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

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