**Angles and Triangles**

**Classifying Angles **

**Classifying Triangles by Angles**

**Classifying Triangles By Sides**

**Example: Classifying a Triangle**

Classify the triangle by its side lengths.

The triangle has no sides of equal length. So, it is a scalene triangle.

**Example: ****Classifying a Triangle**

Classify the triangle by its angles and by its side lengths.

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The triangle has one right angle and two sides of equal length. So, it is a right isosceles triangle.

**Remember that the sum of the angle measures in the triangle is 180 ^{o}. This is true for all triangles.**

**Finding an Unknown Angle Measure**

Find the value of *x* and then classify the triangle by its angles.

**Solution**

The sum of the angle measures in a triangle is 180 degrees.

The triangle has one obtuse angle, so it is an obtuse triangle.

**Guided Practice (Ask your tutor for help.) Find the value of **

*x*and then classify the triangle by its angles.

**1 **

**2**

**3 Complete the statement.**

**A(n) _?_ triangle has no sides of equal length.**

**4 Classify the triangle by its side lengths.**

**a. **

**b. **

**c.**

** **

**5 Describe and correct the error in the solution.**

**6 Estimation**

**The referee is making calls during a hockey game.**

**Classify the angle made by his arms as acute, obtuse, or right.**

**7 Find the value of ***x*. Classify the triangle by its angles.

**8 Can the angles in a triangle have the measures given? Explain.**

**9 Find the value of x.**

**A. ****3 cm B. **

**4 cm**

C.

C.

**7 cm**

D. 10 cm

D. 10 cm

**10 If the two side edges of this gable are the same length, what kind of triangle is formed? Explain.**

**Answers**

1. 40^{o}, obtuse

2. 90^{o}, right

3. scalene

4a. equilateral

4b. isosceles

4c. scalene

5. An acute triangle has 3 acute angles, not just 1. The figure contains a right angle and is therefore a right triangle.

6. obtuse

7. 58^{o}, acute

8. Yes, because the measures add up to 180^{o}.

9. C

10. The triangle would be isosceles, because isosceles triangles have two sides the same length.