Can Three Sticks Meet?

Part of the Triangles section of Coddy's Geometry journey. Lesson 7 of 63.

Take three sticks and try to make a triangle with them. Sometimes it works, and sometimes the two shorter sticks cannot reach each other across the long one. Which happens depends only on the lengths.

Lay the longest stick down. The other two hang from its ends and must meet above it. If together they are shorter than the long stick, they never reach each other, however you swing them. Sticks of 2, 3 and 7 fail, because 2 + 3 = 5 is less than 7.

This is the triangle inequality: any two sides of a triangle add up to more than the third. With the longest side it is the only check you need, because the other two pairs include the longest side and pass automatically.

Challenge

Sticks AC and BC hang from the ends of AB. Drag the point C around: towards AB, below it, far away. Watch how AC + BC compares with AB. Then press Check.

Try it yourself

$Drag the figure and watch$

Drag the figure and watch

Test yourself

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

All lessons in Triangles

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