Triangle Inequality

• ## Triangle Inequality

Grade: 6th to 8th, High School

Sometimes, three straight line segments will form a triangle. And sometimes, they won't. How do you know when they will or won't? This activity lets you explore that question.

### How to Use

Change the length of the segments by dragging the red (right) endpoint of any segment.

### Exploration

Set the length of the first segment to 5.0, and change the length of the second segment to 10.0. Now, change the length of the third segment.

• For what lengths of the third segment will a triangle be formed?
• For what values will the third line segment be too short to form a triangle?
• For what values will it be too long?

Now, change the first two segments to whatever lengths you like, and conduct the same investigation with the third segment. If necessary, repeat this several times until you identify a pattern.

Can you find a general rule that will let you determine whether or not a triangle can be formed, given any three segments?

### Objectives and Standards

NCTM Standards and Expectations
• Geometry / Measurement
• Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
• 6-8
• High School (9-12)
• Geometry