# 8.10.5. Classification of Triangles According to Their Angles

Given that is a rhombus in which cm and cm, what is the type of according to its angles?

• Aan acute triangle
• Ban obtuse triangle
• Ca right-angled triangle

### Example

Given that is a rhombus in which cm and cm, what is the type of according to its angles?

### Solution

Step 1: Find the side lengths of the rhombus.

Let represent the point of intersection of the diagonals.

The diagonals of a rhombus form angles. So, .

The diagonals of a rhombus also bisect each other. Therefore,

To find the length of , use Pythagoras' theorem. Substitute the known lengths in , and solve for the length of . (Approximate to the nearest hundredth.)

All sides of a rhombus are of equal length. Therefore,

Step 2: Classify .

If the square length of a triangle's longest side is less than the sum of the square lengths of the other two sides, then the triangle is acute. (Approximate to the nearest hundredth.)

Given that and therefore

Hence, is an acute triangle.

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