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Testing a Triangle

Part of the Triangles section of Coddy's Geometry journey. Lesson 34 of 63.

To test whether three lengths make a right triangle, find the longest one: that is the only side the right angle could face. Square the two shorter sides and add them, then compare with the square of the longest.

$Three triangles labelled 5, 12, 13 and 6, 7, 9 and 3, 4, 6$

For 5, 12 and 13: 5^2 + 12^2 = 25 + 144 = 169, and 13² is 169. Equal, so the first triangle is right. For 6, 7 and 9: 36 + 49 = 85, but 9² is 81, so that one is not. Neither is 3, 4, 6: 9 + 16 = 25, and 6² is 36. Pick the longest side by its length, never by where it is drawn.

Challenge

Each triangle has its three side lengths written on it, and none is marked with a square. Test each one with the squares of its sides, then tap the right triangle and press Check.

Try it yourself

$Find the right part on the figure$

Find the right part on the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

1Sides and Names

Three Sides, Three Corners Sorting by Sides Naming by Angles Ticks into Equations The Longest Side Recap: Sorting Triangles

4Area of a Triangle

Half the Rectangle Height Is Not a Side Right Triangle Area Finding the Height Any Side Can Be the Base Recap: Area

7Is It Right?

The ConverseTesting a TriangleAcute or Obtuse?Sorting by the Test Recap: Right or Not

10Scale in the World

Shadows Across the River Nested Triangles A Side with an Expression Recap: Scale in the World

2The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side The Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools