The Pythagorean Theorem: Grade 8 Math Quiz – PDF Download
Ten multiple-choice questions on the Pythagorean Theorem (8.G.B.6 and 8.G.B.7). Find missing sides, test triangles with the converse, and handle ladders, screens and boxes. Pick the single best answer, then read the explanation to see which mistake each wrong choice matches.
Grade 8Common Core: 8.G.B.6 · 8.G.B.7
🎯 The Pythagorean Theorem – Grade 8 math quiz
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Question 1
What is the length of the hypotenuse?A right triangle with legs 7 and 24.
A31
B17
C25
D625
Question 2
A right triangle has a hypotenuse of 20 and one leg of 12. What is the other leg?
A8
B16
C23.3
D32
Question 3
Which set of side lengths forms a right triangle?
A8, 12, 15
B9, 40, 41
C6, 9, 11
D10, 15, 18
Question 4
A 10-ft ladder has its base 6 ft from a wall. How high up the wall does it reach?A ladder leaning on a wall.
A4 ft
B11.7 ft
C64 ft
D8 ft
Question 5
A TV screen is 16 in. wide and 12 in. tall. How long is the diagonal?
A28 in
B4 in
C20 in
D400 in
Question 6
The legs of a right triangle are 3 and 5. What is the hypotenuse to the nearest tenth?
A8.0
B5.8
C4.0
D34.0
Question 7
A square with side 11 contains four right triangles with legs 5 and 6. What is the area of the tilted square in the middle?Four triangles with legs 5 and 6.
A91
B121
C60
D61
Question 8
What is the length of the space diagonal of a box that is 2 by 3 by 6?A box.
A7
B11
C49
D3.6
Question 9
A triangle has sides 6 in., 8 in. and 9 in. Which statement is correct?
AIt is a right triangle, because 6 + 8 is greater than 9.
BIt is a right triangle, because 9 is its longest side.
CIt is not a right triangle, because 6 squared plus 8 squared is 100, not 81.
DIt is a right triangle, because all three sides are whole numbers.
Question 10
Liam walks 0.6 mi west and then 0.8 mi south. How far is he from his start in a straight line?
A1.0 mi
B1.4 mi
C0.2 mi
D0.5 mi
🎉 Quiz complete!
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Remember:
Standards 8.G.B.6 and 8.G.B.7: explain a proof of the theorem and its converse, then apply it in two and three dimensions.
The hypotenuse is opposite the right angle and is always the longest side.
To find a missing side, substitute into \(a^{2}+b^{2}=c^{2}\), then take a positive square root.
Converse: if \(a^{2}+b^{2}=c^{2}\) holds for the sides of a triangle, it is a right triangle.
The diagonal of a box satisfies \(d^{2}=l^{2}+w^{2}+h^{2}\).
