# 7.7.3. Triangles

Given that is a triangle in which , determine the triangle’s type according to its angles without finding their measures.

• Aacute-angled triangle
• Bright-angled triangle
• Cobtuse-angled triangle

### Example

Given that is a triangle in which , determine the triangle’s type according to its angles without finding their measures.

### Solution

A triangle is acute-angled if each angle measure is less than half of the triangle's total angle measures. It is obtuse-angled if one of its angles is greater than half of its total angle measures. It is right-angled if one of its angle measures is exactly half of its angle measures.

We can use the concept of the sum of parts to solve this problem, with parts, parts, and parts. Find half of the triangle's angle measures (as a number of parts).

None of the angle measures is 7.5 parts or greater. Therefore, the triangle is acute-angled.

A triangle's shortest side lies opposite its greatest angle. is the greatest angle measure (because 6 parts > 5 parts > 4 parts). Therefore, the triangle is acute-angled at .

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