Types of Triangles

Read the answer names to see whether to compare angles or sides.

• A right-angled triangle has a right angle, often marked with a small square.
• An obtuse-angled triangle has one angle larger than a right angle.
• An acute-angled triangle has all angles smaller than a right angle.
• An equilateral triangle has all 3 sides equal.
• An isosceles triangle has two equal sides.
• A scalene triangle has all sides of different lengths.

Matching marks on sides mean matching lengths. Turning a triangle does not change its type.

A triangle’s perimeter is the sum of all three side lengths. Add the three lengths stated in the question.

For example, sides of 4 cm, 5 cm and 6 cm give 4 + 5 + 6 = 15 cm. Add the lengths rather than multiplying them.

A triangle is classified by its greatest angle.

• If one angle is exactly 90°, the triangle is right-angled.
• If one angle is greater than 90°, the triangle is obtuse-angled.
• If all three angles are less than 90°, the triangle is acute-angled.

Find the greatest given angle and use these conditions to select the triangle type.

A triangle is classified by its greatest angle.

• If one angle is exactly 90°, the triangle is right-angled.
• If one angle is greater than 90°, the triangle is obtuse-angled.
• If all three angles are less than 90°, the triangle is acute-angled.

Find the greatest given angle and use these conditions to select the triangle type.

The interior angles of every triangle always add up to 180°.

1. Add the measures of the two known angles.
2. Subtract their sum from 180°.
3. The remaining value is the third angle of the triangle.

Formula: third angle = 180° − first angle − second angle.

A triangle is classified by comparing the lengths of all three sides.

• If all three sides are equal, the triangle is equilateral.
• If exactly two sides are equal, the triangle is isosceles.
• If all three side lengths are different, the triangle is scalene.

Compare the three given lengths and select the matching type.

The fence goes around all three sides of the triangular bed. Find the triangle’s perimeter.

Add the three side lengths. The answer is in metres; you do not need the bed’s area.

Compare the lengths of all three sides.

• If all three sides are equal, choose equilateral.
• If exactly two sides are equal, choose isosceles.
• If all three sides are different, choose scalene.

The question is about sides, so you do not need to calculate angles.

The fence goes around all three sides of the triangular bed. Find the triangle’s perimeter.

Add the three side lengths. The answer is in metres; you do not need the bed’s area.

For three segments to form a triangle, the third side must be shorter than the sum of the two given sides and longer than their difference.

1. Add the given side lengths: a + b. The third side must be shorter than this sum.
2. Find the difference between the given side lengths: |a − b|. The third side must be longer than this difference.
3. Choose the listed length that satisfies both conditions.

Rule: if the third side has length c, then |a − b| < c < a + b.