1. Classify angles and triangles 10.3
Ray- Extend in one direction
Line- Extends in two directions
Angles- Two rays have the same endpoint
Vertex-The common endpoint
Sides- the two rays that make up the angle
The symbol means angle
You can classify angles four ways
Use the vertex and a point <ABC or <CBA
Use the vertex only <B
Use a number <1
Classify angles and triangles 10.3

3. Name the angle below in two ways
Name the angle below in two ways. Then classify it as acute, right, obtuse, or straight.
A. JKL, K; acute
B. LKJ, K; right
C. JKL, K; obtuse
D. LKJ, J; obtuse

4. Classify Angles A. Matching F. B. C. D. E. 1. Acute ____ 2. Right ____
3. Obtuse ____
4. Straight ____
5. Vertical ____
6. Congruent ____ A B

5. Key Concept 3

6. Example 3 CYP Classify the triangle by its angles and by its sides.
A. acute scalene
B. acute isosceles
C. obtuse scalene
D. obtuse isosceles

8. Example 4 Classify Triangles
Classify the triangle by its angles and by its sides.
The triangle has all acute angles and two congruent sides.
Answer: It is an acute isosceles triangle.

9. Example 3 Classify Triangles
Classify the triangle by its angles and by its sides.
The triangle has a right angle and no congruent sides.
Answer: It is a right scalene triangle.

10. Example 4 CYP Classify the triangle by its angles and by its sides.
A. acute scalene
B. acute isosceles
C. right scalene
D. right isosceles

11. Key Concept

12. Example 1 Find Angle Measures
PARK The city park shown is in the shape of a triangle. Find the value of x.
x = 180 Write the equation.
x + 72 = 180
– – 72
x = 108
Answer: The value of x is 108°.

13. Example 1 CYP
STONES The paver stone shown below is in the shape of a triangle. Find the value of x.
A. 39°
B. 56°
C. 73°
D. 146°

14. Example 2 Use Ratios to Find Angle Measures
The measures of the angles of ΔDEF are in the ratio 1:2:3. What are the measures of the angles?

15. Example 2 Use Ratios to Find Angle Measures
x + 2x + 3x = 180 Write the equation.
6x = 180 Combine like terms.
x = 30 Simplify.
Since x = 30, 2x = 2(30) or 60, and 3x = 3(30) or 90.
Answer: The measures of the angles are 30°, 60°, and 90°.

16. Example 2 CYP
The measures of the angles of ΔQRS are in the ratio 1:3:6. What are the measures of the angles?
A. 18°, 36°, 54°
B. 18°, 54°, 108°
C. 15°, 45°, 90°
D. 30°, 60°, 90°