1. 1.4 Measure and Classify Angles
You will name, measure and classify angles.

2. Classifying Angles Acute angle: between 0 and 90
Right angle: exactly 90 degrees
Symbol:
Obtuse Angle: between 90 and 180
Straight angle: exactly 180 degrees

3. Angles Naming Angles Angle Bisector
Use 3 capital letters – Vertex in the middle
Can use one capital letter if it is the vertex and it is obvious which angle you are referring to
Can use the number located inside the angle
Angle Bisector
Divides the angle into 2 congruent parts

4. Naming angles
Name this angle three different ways

5. Naming angles
Name this angle three different ways

6. Naming angles
Name this angle four different ways

7. Name this angle in 4 ways

8. Congruent Angles
Have the same angle measure

9. Congruent Angles Can be marked using the same number of hash marks. HW F Q

10. Angle Addition Postulate
Smaller angles can be added together to form larger angles if they share a common vertex.

11. Given that the m<LKN=145⁰, find the m<LKM and m<MKN

12. GUIDED PRACTICE
for Example 3
Find the indicated angle measures.
Given that <KLM is a straight angle, find x and m< NLM.

13. GUIDED PRACTICE
for Example 3
4. Given that < EFG is a right angle, find x and m< HFG.

14. Homework
Page 28 # 4 – 40 even
Honors: also # 42, 44, 48, 49, 50

15. EXAMPLE 2
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.

16. Angle Addition Postulate
When two angles share a ray, a
Part+ Part = Whole or Little + Little = Big
Very similar to segment addition Postulate

17. Congruent Angles Angles that have the same measure
Angle measures are equal: m<A=m<B
The measure of angle A is equal to the measure of angle B
Angle measures are congruent: <A <B
Angle A is congruent to angle B
When talking about measures, use equal sign. When talking about congruency, use congruent sign

18. EXAMPLE 4
Identify congruent angles
The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what is m<GKL?

19. GUIDED PRACTICE
for Example 4
Use the diagram shown.
5. Identify all pairs of congruent angles in the diagram.

20. GUIDED PRACTICE
for Example 4
Use the diagram shown.
6. In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = Find the other angle measures in the diagram.

21. Angle Formed by two rays that meet at an endpoint
Rays are considered sides of an angle
What is the vertex? What rays form the angle?

22. Vertex of an Angle Where the sides of an angle meet.
When naming an angle, vertex goes in the middle
Name the three angles in the diagram.

23. Angle bisector
A ray that divides an angle into two angles that are congruent (equal)
In the diagram at the right, YW bisects < XYZ, and m< XYW = 18. Find m< XYZ.

24. Protractor Postulate
The rays of an angle can be matched one to one with real numbers from 0 to 180
The measure of an angle is equal to the absolute value of the difference between the real number of the rays (much like the segment addition postulate)