Grade 8 · Math

8th grade Is it a right triangle? (the converse) worksheet

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Is it a right triangle? (the converse)

Grade 8 Math Worksheet

NameDate

Circle the best answer.

1.
Esme cuts a triangle from paper with sides of 50, 14 and 48 cm. Is it a right triangle?
- You cannot tell without measuring the angles.
- Yes, it is a right triangle: the squares on the two shorter sides add up to the square on the longest.
- Yes, it is a right triangle, because the two shorter sides together are longer than the longest.
- No, it is not a right triangle: the squares on the two shorter sides do not add up to the square on the longest.
2.
Jun's felt triangle has sides of 11, 15 and 10 inches. Is it a right triangle?
- Yes, it is a right triangle, because the two shorter sides together are longer than the longest.
- You cannot tell without measuring the angles.
- No, it is not a right triangle: the squares on the two shorter sides do not add up to the square on the longest.
- Yes, it is a right triangle: the squares on the two shorter sides add up to the square on the longest, so it has a square corner.
3.
Luz's poster triangle has sides of 13, 18 and 12 cm, drawn in bright crayon. Is it a right triangle?
- You cannot tell without measuring the angles.
- Yes, it is a right triangle, because the two shorter sides together are longer than the longest.
- No, it is not a right triangle: the squares on the two shorter sides do not add up to the square on the longest.
- Yes, it is a right triangle: the squares on the two shorter sides add up to the square on the longest.
4.
Milo's math book shows a triangle with sides 48, 52 and 20 inches, with no angle marked. Is it a right triangle?
- Yes, it is a right triangle, because the two shorter sides together are longer than the longest.
- Yes, it is a right triangle: the squares on the two shorter sides add up to the square on the longest.
- You cannot tell without measuring the angles.
- No, it is not a right triangle: the squares on the two shorter sides do not add up to the square on the longest.
5.
16, 63 and 65; 9, 11 and 14; 7, 8 and 9. Ren's math book gives three triangles' sides in inches. Which one is a right triangle?
- Sides 7, 8 and 9
- Sides 9, 11 and 14
- Sides 16, 63 and 65
6.
24, 45 and 51; 9, 10 and 14; 4, 5 and 6. Tala's robot offers three sets of sides, in cm, and waits politely. Which set makes a right triangle?
- Sides 4, 5 and 6
- Sides 9, 10 and 14
- Sides 24, 45 and 51
7.
Zee builds a model door frame, 45 cm by 60 cm, and the diagonal measures 75 cm. Is the corner square?
- Yes, the corner is square, because the diagonal is the longest side.
- No, the corner is not square: the squares on the two sides do not add up to the square on the diagonal.
- Yes, the corner is square: the squares on the two sides add up to the square on the diagonal.
- You cannot tell without a tool that measures angles.
8.
Ari checks a table top 40 inches by 42 inches; its diagonal is 57 inches. Is the corner square?
- Yes, the corner is square: the squares on the two sides add up to the square on the diagonal, so it is a right angle.
- Yes, the corner is square, because the diagonal is the longest side.
- No, the corner is not square: the squares on the two sides do not add up to the square on the diagonal.
- You cannot tell without a tool that measures angles.
9.
Bo's class rug is 24 by 70 inches, and the diagonal is 74 inches. Is the corner square?
- No, the corner is not square: the squares on the two sides do not add up to the square on the diagonal.
- You cannot tell without a tool that measures angles.
- Yes, the corner is square, because the diagonal is the longest side.
- Yes, the corner is square: the squares on the two sides add up to the square on the diagonal.
10.
Esme measures a window 36 by 48 inches; the diagonal is 61 inches. Is the corner square?
- Yes, the corner is square: the squares on the two sides add up to the square on the diagonal.
- You cannot tell without a tool that measures angles.
- Yes, the corner is square, because the diagonal is the longest side.
- No, the corner is not square: the squares on the two sides do not add up to the square on the diagonal.

8th grade Is it a right triangle? (the converse) worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Is it a right triangle? (the converse). Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the longest side, wherever it is listed, and square every side.
I can decide whether a triangle has a right angle: the two smaller squares must add up to exactly the biggest.
I can say where the right angle is (across from the longest side) and check a square corner in a real frame.

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

Words to know

right triangle: A triangle with one square corner.

converse: The theorem turned around: if the squares add up, there is a right angle.

longest side: The side whose square must equal the other two squares together.

square corner: A right angle, like the corner of a door frame.

near miss: Squares that come close but are not equal: not a right triangle.

Common mistakes

Your child added the side lengths instead of their squares. The test for a right triangle adds the squares on the two shorter sides. Try it on a 3, 4, 5 triangle: 9 + 16 = 25.

Your child squared and added, but used the longest side. The test adds the squares on the two shorter sides and compares them with the square on the longest side. Point to the longest side together first.

Your child said the triangle is not right when the two smaller squares add up exactly to the biggest. Equal sums always mean a right angle. Add the two smaller squares together and compare.

Questions parents ask

What is the most common mistake with is it a right triangle? (the converse)?

Your child added the side lengths instead of their squares. The test for a right triangle adds the squares on the two shorter sides. Try it on a 3, 4, 5 triangle: 9 + 16 = 25.

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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