Classify The Following Triangle Check All That Apply

How to Classify a Triangle

A triangle is a polygon with three sides and three angles. Triangles can be classified by their side lengths and by their angle measures.

By side length

Triangles can be classified as equilateral, isosceles, or scalene.

• Equilateral triangles have all three sides of equal length.
• Isosceles triangles have two sides of equal length.
• Scalene triangles have all three sides of different lengths.

By angle measure

Triangles can be classified as acute, right, or obtuse.

• Acute triangles have all three angles less than 90 degrees.
• Right triangles have one angle that is 90 degrees.
• Obtuse triangles have one angle that is greater than 90 degrees.

Questions

Here are some questions that can be used to classify a triangle:

• Are all three sides of equal length?
• Are two sides of equal length?
• What is the measure of the largest angle?

Answers

Here are some answers to the questions above:

• If all three sides of a triangle are equal, then the triangle is equilateral.
• If two sides of a triangle are equal, then the triangle is isosceles.
• If the measure of the largest angle in a triangle is 90 degrees, then the triangle is right.

Examples

Here are some examples of triangles classified by side length and angle measure:

• Equilateral triangle: All three sides are equal in length, and all three angles are acute.
• Isosceles triangle: Two sides are equal in length, and the third side is different in length. The angles opposite the equal sides are equal in measure, and the angle opposite the unequal side is different in measure.
• Scalene triangle: All three sides are different in length, and all three angles are acute.
• Right triangle: One angle is 90 degrees, and the other two angles are acute.
• Obtuse triangle: One angle is greater than 90 degrees, and the other two angles are acute.

Conclusion

Triangles can be classified by their side lengths and by their angle measures. By understanding how to classify triangles, we can better understand the properties of triangles and how they can be used in geometry.