Grade 7 Mathematics โ Pythagorean Relationship Quiz
1. Which of the following can be used to make a right angle triangle?
2. Find the length of the side of a triangle whose two shorter sides are 8cm and 6 cm.
3. What is the length of the longest side of a triangle given the other two sides as 3cm and 4cm?
4. Which Pythagorean theorem equation is true ?
5. Which of the following are right angled triangle?
6. ABC is a right triangle. AC is its hypotenuse. Length of side AB is 2โ5. Side BC is twice of side AB. Find the length of AC.
7. The hypotenuse of a right triangle is 6 cm. Its area is 9 cm2. Find its sides.
8. One side of a right triangle is 4โ10cm. Find the length of its other side if the hypotenuse is 13 cm.
9. In a right triangle ABC, length of the medians to the sides AB and BC are 2โ61 โ and โ601 respectively. Find the length of its hypotenuse.
10. In a right triangle, the longest side is 8 cm. One of the remaining sides is 4โ3 cm long. Find the length of the other side.
11. The first side of a right triangle is shorter than the second side by 1 cm. It is longer than the third side by 31 cm. Find the sides of the triangle.
12. The perimeter of a right triangle is equal to 30 cm. The length of one of its sides is 10 cm. Find its hypotenuse.
13. In a right triangle, two sides are equal. The longest side is 7โ2 cm, find the remaining sides
14. What is the Pythagorean Theorem?
15. Which of the listed side lengths CAN be sides of a right triangle?
16. Which of the listed sides CAN be sides of a right triangle?
17. Calculate the length of the hypotenuse of a right angled triangle given the two sides being 9cm and 40cm.
18. Calculate the length of the third side of right angle triangle given the longest and one of the other smaller sides as 15cm and 12cm.
19. In the evening, the shadow of an object is very long due to the low position of the Sun. A 20m height lamp post makes a 99m long shadow. What is the distance from the top of the pole to the top of its shadow?
20. Use the Pythagorean Theorem to find the value of the hypotenuse.a=3cm b=4cm.
21. The longest side of a right triangle is called the...............
22. When finding the hypotenuse, you must take the ______________ the value c.
23. To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
24. What kind of triangles does the Pythagorean Theorem work with?
25. The hypotenuse is always.............
26. c= 97, b= 72, a=?
27. What is the name for side c?
28. John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?
29. You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
30. A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?
31. A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?
32. An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?
33. In a computer catalog, a computer monitor is listed as being 27 inches. This distance is the diagonal distance across the screen. If the screen measures 15 inches in height, what is the actual width of the screen to the nearest inch?
34. What is a logical mathematical argument in which every statement of fact is supported by a reason?
35. A right triangle has side lengths of 4 centimeters and 5 centimeters. What is the length of the hypotenuse?
36. What is true about the hypotenuse?
37. What conclusion can you draw if you plug the measure three sides of a triangle into the Pythagorean Theorem?
38. Why do we use the Pythagorean Theorem?
39. What is the hypotenuse (c)?
40. What are the "legs" of a triangle (a + b)?
41. What is an example of squaring a number?
42. What is the Pythagorean relationship used for in Mathematics?
The Pythagorean relationship is a fundamental concept used to solve for the sides of right-angled triangles.
43. In a right-angled triangle, which side is known as the hypotenuse?
The hypotenuse is the side opposite the right angle and is the longest side in a right-angled triangle.
44. If the two shorter sides of a right triangle measure 3 and 4 units respectively, what would be the length of the hypotenuse according to the Pythagorean relationship?
According to the Pythagorean relationship (a^2 + b^2 = c^2), the hypotenuse would be โ(3^2 + 4^2) = 5 units.
45. Which of the following is the correct formula for the Pythagorean relationship?
The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
46. If a right-angled triangle has sides of length 6, 8, and x, what is the length of x according to the Pythagorean relationship?
Using the Pythagorean relationship a^2 + b^2 = c^2, we have 6^2 + 8^2 = x^2, which simplifies to 36 + 64 = x^2, x^2 = 100, x = โ100 = 10 units.
47. What is the Pythagorean relationship between the sides a, b, and c of a right-angled triangle?
The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
48. If the two shorter sides of a right triangle measure 5 and 12 units respectively, what would be the length of the hypotenuse according to the Pythagorean relationship?
Using the Pythagorean relationship a^2 + b^2 = c^2, we have 5^2 + 12^2 = c^2, which simplifies to 25 + 144 = c^2, c^2 = 169, c = โ169 = 13 units.
49. What is the longest side of a right-angled triangle called?
The hypotenuse is the longest side in a right-angled triangle and is opposite the right angle.
50. If a right-angled triangle has sides of length 9, 12, and x, what is the length of x according to the Pythagorean relationship?
Using the Pythagorean relationship a^2 + b^2 = c^2, we have 9^2 + 12^2 = x^2, which simplifies to 81 + 144 = x^2, x^2 = 225, x = โ225 = 15 units.
51. Which theorem is used to find the relationship between the sides of a right-angled triangle?
The Pythagorean theorem is used to find the relationship between the sides of a right-angled triangle.
52. If the two shorter sides of a right triangle measure 7 and 24 units respectively, what would be the length of the hypotenuse according to the Pythagorean relationship?
Using the Pythagorean relationship a^2 + b^2 = c^2, we have 7^2 + 24^2 = c^2, which simplifies to 49 + 576 = c^2, c^2 = 625, c = โ625 = 25 units.
53. What is the Pythagorean relationship between the sides of a right triangle?
The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.