📐 Pythagorean Theorem & Right Triangles
Master the Pythagorean theorem and its applications in Grade 8 mathematics. This quiz challenges you to find missing side lengths in right triangles, verify whether triangles are right triangles, and apply the theorem to real-world scenarios in construction, navigation, and measurement. **What you'll learn:** - Apply $a^2 + b^2 = c^2$ to find unknown side lengths - Verify if a triangle is a right triangle using the converse theorem - Solve multi-step problems involving the Pythagorean theorem - Use the theorem in practical contexts (distance, construction, routes)
Questions in this quiz
Answers hidden — play to find out.
- Question 1
In a right triangle, the two legs measure 5 cm and 12 cm. What is the length of the hypotenuse?
- Question 2
The Pythagorean theorem only applies to isosceles right triangles.
- Question 3
A right triangle has legs of 9 m and 12 m. What is the length of the hypotenuse to the nearest tenth of a metre?
- Question 4
Which set of side lengths does NOT form a right triangle?
- Question 5
If a triangle has sides of 3, 4, and 5 units, it is a right triangle.
- Question 6
A right triangle has a hypotenuse of 20 cm and one leg of 12 cm. What is the length of the other leg?
- Question 7
A ladder leans against a wall. The ladder is 10 m long, and its base is 6 m from the wall. How high up the wall does the ladder reach, to the nearest tenth of a metre?
- Question 8
In a right triangle, the hypotenuse is always the longest side.
- Question 9
A square garden has sides of 15 m. If you walk diagonally across the garden from one corner to the opposite corner, how far do you walk, to the nearest tenth of a metre?
- Question 10
A right triangle has legs of 7 cm and cm. What is the length of the hypotenuse?
- Question 11
A 25 m ladder leans against a building wall at an angle. The foot of the ladder is 7 m away from the wall. Does the ladder reach a height of 24 m?
- Question 12
A triangle with sides 10 cm, 15 cm, and 20 cm is a right triangle.
- Question 13
Two towns are connected by roads that meet at a right angle. Town A to Town B is 12 km, and Town B to Town C is 9 km, where the angle at B is 90°. What is the straight-line distance from Town A to Town C?
- Question 14
A right triangle has legs of 8 inches and 15 inches. If you build a similar right triangle with a scale factor of 2, what is the hypotenuse of the new triangle?
- Question 15
Which of the following is NOT a Pythagorean triple?