  # Identify Right-Angled Triangles

In this worksheet, students will use the converse of Pythagoras' Theorem to determine whether or not a triangle is right-angled. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Popular topics:   Geometry worksheets

Difficulty level:   #### Worksheet Overview

Pythagoras' theorem states that in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Thus in the above right-angled triangle a2 + b2  = c2

If a triangle of sides a, b and c is such that a2 + b2 = c2, then the triangle is right-angled.

Example 1

A triangle has sides of length 6 cm, 8 cm and 9 cm.

Is it right-angled?

First, pick the two shorter sides, square them and then add:

62 + 82 = 36 + 64 = 100

Then square the longest side:

92 = 81

So 62 + 82 ≠ 92 and the triangle is therefore not right-angled.

Example 2

A triangle has sides of length 5 cm, 13 cm and 12 cm.

Is it right-angled?

First, pick the two shorter sides, square them and then add:

52 + 122 = 25 + 144 = 169

Then square the longest side:

132 = 169

So 52 + 122 = 132 and the triangle is therefore right-angled.

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