The Pythagorean Theorem: math test, Grade 8 – download the PDF

1 Missing sides / 4 pts

Find the missing side of each right triangle. Give an exact value, and round to the nearest hundredth when it is not a whole number.

1. Legs 15 cm and 20 cm: find the hypotenuse.
2. Hypotenuse 37 m and one leg 12 m: find the other leg.
3. Legs 4 in and 9 in: find the hypotenuse.

2 The converse / 3 pts

Decide whether each triangle is a right triangle. Show your work.

1. Sides 16 cm, 30 cm, 34 cm
2. Sides 11 cm, 13 cm, 17 cm

3 Points in the plane / 4 pts

Let \(P(-2, -1)\), \(Q(10, 8)\) and \(R(10, -1)\).

1. Find the distance \(PQ\). (2 pts)
2. Explain why triangle \(PRQ\) has a right angle at \(R\), and find its perimeter. (2 pts)

4 A ladder and a window / 4 pts

A 25 ft ladder reaches a window 24 ft above the ground.

1. How far is the foot of the ladder from the wall? (2 pts)
2. The foot is pulled out to 15 ft from the wall. How high does the ladder reach now? (2 pts)

5 A storage crate / 3 pts

A crate measures 9 in by 12 in by 20 in.

1. Find the diagonal of its 9 in by 12 in face. (1 pt)
2. Find the length of its space diagonal. (2 pts)

6 True or false? / 2 pts

True or false: “A triangle with sides 1.2 cm, 1.6 cm and 2 cm is a right triangle.” Justify your answer.