1. Chapter 1.4 Notes: Measure and Classify Angles Goal: You will name, measure, and classify angles.

2. An angle consists of two different rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. Name the angle above: _____, ______, ______ ____________ is the vertex of the angle.

3. Ex.1: Name the three angles in the diagram.

4. Ex.2: Name the three angles in the diagram. M O N P

5. Classifying Angles: Angles can be classified as acute, right, obtuse, and straight. Acute angles have a measure greater than 0 and less than 90. Right angles have a measure of 90. Obtuse angles have a measure greater than 90 and less than 180. Straight angles have a measure of 180.

6. Measuring Angles: A protractor can be used to approximate the measure of an angle. An angle is measured in units called degrees ( o ).

7. Postulate 3 Protractor Postulate: Consider and a point A on one side of. The rays of the form can be matched one to one with the real numbers from 0 to 180. The measure of is equal to the absolute value of the difference between the real numbers for and. A O B

8. EXAMPLE 3 Measure and classify angles Use the diagram to find the measure of the indicated angle. Then classify the angle. a. KHJ b. GHK c. GHJ d. GHL SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

9. Postulate 4 Angle Addition Postulate: If P is in the interior of, then the measure of is equal to the sum of the measures of and. If P is in the interior of, then

10. Ex.4: Given that, find and.

11. Ex.5: If find and

12. Ex.6: Given that is a straight angle, find and.

13. Ex.7: Given that is a right angle, find and.

14. Congruent Angles: Two angles are congruent angles if they have the same measure. Angle measures ar equal Angles are congruent

15. Ex.8: The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If, what is ?

16. Ex.9: Use the diagram below. a. Identify all pairs of congruent angles. b.,, and. Find the other angle measures in the diagram.

17. An angle bisector is a ray that divides an angle into two angles that are congruent. Ex.10: In the diagram below, bisects, and. Find.