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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Pythagoras 1 (Questions)

This Math quiz is called 'Shapes - Pythagoras 1' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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This Shapes quiz looks at the special number relationship linking the lengths of the sides of a right triangle. This relationship is named after the Greek mathematician, Pythagoras. You may find it helpful to draw some diagrams.

Get your pencil and paper out and see how well you do in this quiz.

1. If the longest side of a right triangle is c cm and the other sides are a cm and b cm, Pythagoras' Theorem states that .......
[ ] a2 x b2 = c2
[ ] (a + b)2 = c2
[ ] a2 + b2 = c2
[ ] a2 - b2 = c2
2. In a right triangle the sides forming the 90° angle are 6 cm and 8 cm. What is the length of the third side?
[ ] 10 cm
[ ] 12 cm
[ ] 14 cm
[ ] 16 cm
3. The following sets of numbers represent the lengths of the sides of a triangle. Which is not a right triangle?
[ ] 15, 20, 25
[ ] 18, 24, 30
[ ] 16, 30, 36
[ ] 15, 36, 39
4. A triangle has sides of length 4 cm, 5 cm and 6 cm. Which of these statements is not true?
[ ] The three angles add up to 180°
[ ] All three angles are acute
[ ] The triangle is scalene
[ ] The largest angle is 90°
5. The hypotenuse of a right triangle is 26 cm. One of the shorter sides is 10 cm. How long is the third side?
[ ] 30 cm
[ ] 24 cm
[ ] 16 cm
[ ] 8 cm
6. A right-angled isosceles triangle has hypotenuse of length 15 cm. What are the angles at either end of the hypotenuse?
[ ] 15° and 75°
[ ] 30° and 60°
[ ] 45° and 45°
[ ] 20° and 70°
7. A rectangle has length 2.4 m and width 0.7 m. How long is its diagonal?
[ ] 2.0 m
[ ] 2.5 m
[ ] 3.0 m
[ ] 3.5 m
8. The foot of a ladder of length 3.75 m is 1.4 m away from a vertical wall. How high up the wall will the ladder reach (to the nearest 1 cm)?
[ ] 3.84 m
[ ] 3.48 m
[ ] 3.24 m
[ ] 3.18 m
9. The cross-section of a porch roof is an isosceles triangle with height 0.8 m and base 3.0 m. How long is each sloping roof section?
[ ] 3.1 m
[ ] 2.3 m
[ ] 1.9 m
[ ] 1.7 m
10. In a triangle, base 25 cm and height 12 cm, the perpendicular from the base to the opposite vertex divides the base in the ratio 3:2. How long are the other two sides (to 1dp)?
[ ] 15.6 cm and 19.2 cm
[ ] 16.3 cm and 18.9 cm
[ ] 15.6 cm and 16.3 cm
[ ] 18.9 cm and 19.2 cm
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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Pythagoras 1 (Answers)
1. If the longest side of a right triangle is c cm and the other sides are a cm and b cm, Pythagoras' Theorem states that .......
[ ] a2 x b2 = c2
[ ] (a + b)2 = c2
[x] a2 + b2 = c2
[ ] a2 - b2 = c2
Remember, Pythagoras' Theorem only applies to right triangles
2. In a right triangle the sides forming the 90° angle are 6 cm and 8 cm. What is the length of the third side?
[x] 10 cm
[ ] 12 cm
[ ] 14 cm
[ ] 16 cm
36 + 64 = 100; √100 = 10. The longest side in a right triangle is called the hypotenuse
3. The following sets of numbers represent the lengths of the sides of a triangle. Which is not a right triangle?
[ ] 15, 20, 25
[ ] 18, 24, 30
[x] 16, 30, 36
[ ] 15, 36, 39
4. A triangle has sides of length 4 cm, 5 cm and 6 cm. Which of these statements is not true?
[ ] The three angles add up to 180°
[ ] All three angles are acute
[ ] The triangle is scalene
[x] The largest angle is 90°
5. The hypotenuse of a right triangle is 26 cm. One of the shorter sides is 10 cm. How long is the third side?
[ ] 30 cm
[x] 24 cm
[ ] 16 cm
[ ] 8 cm
262 - 102 = 242
6. A right-angled isosceles triangle has hypotenuse of length 15 cm. What are the angles at either end of the hypotenuse?
[ ] 15° and 75°
[ ] 30° and 60°
[x] 45° and 45°
[ ] 20° and 70°
The side length is irrelevant. The only right-angled isosceles triangle has two angles of 45o
7. A rectangle has length 2.4 m and width 0.7 m. How long is its diagonal?
[ ] 2.0 m
[x] 2.5 m
[ ] 3.0 m
[ ] 3.5 m
The diagonal is the hypotenuse of a right triangle
8. The foot of a ladder of length 3.75 m is 1.4 m away from a vertical wall. How high up the wall will the ladder reach (to the nearest 1 cm)?
[ ] 3.84 m
[x] 3.48 m
[ ] 3.24 m
[ ] 3.18 m
This assumes that the ground is perfectly level!
9. The cross-section of a porch roof is an isosceles triangle with height 0.8 m and base 3.0 m. How long is each sloping roof section?
[ ] 3.1 m
[ ] 2.3 m
[ ] 1.9 m
[x] 1.7 m
10. In a triangle, base 25 cm and height 12 cm, the perpendicular from the base to the opposite vertex divides the base in the ratio 3:2. How long are the other two sides (to 1dp)?
[x] 15.6 cm and 19.2 cm
[ ] 16.3 cm and 18.9 cm
[ ] 15.6 cm and 16.3 cm
[ ] 18.9 cm and 19.2 cm
Split the triangle into two right triangles with bases 15 cm and 10 cm
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