The document contains information about classifying angles, complementary and supplementary angles, and vertical angles. It defines different types of angles such as acute, obtuse, right, and straight angles. It provides examples of using properties of angles, such as two angles being complementary if their measures sum to 90 degrees. It discusses how vertical angles have the same measure when two lines intersect.

1. Daily Homework Quiz For use after Lesson 7.3 Use a percent proportion to answer the question. 1 . 28 is what percent of 80 ? 2 . 15 is 5% of what number?

2. Daily Homework Quiz For use after Lesson 7.3 Use a percent proportion to answer the question. 1 . 28 is what percent of 80 ? 2 . 15 is 5% of what number? ANSWER 35% ANSWER 300

3. Chapter 8.1 Lines and Angles

4. Essential Questions Why is it important to be able to identify congruent triangles in everyday life? Where in real life can you use the properties of isosceles and equilateral triangles? How are the relationships between lines and planes used in the real world? What areas in the real world are properties of parallel lines important?

5. Chapter 8 Section 1 Vocabulary 1-14

6. Prerequisite Skills VOCABULARY CHECK Point: a figure without dimensions. Line: a figure that extends without end in two opposite directions. X Y XY CD A Ray: a figure that has one endpoint and extends without end in one direction. C D

7. Plane : A flat surface that extends without end. Angle: a figure formed by two rays that begin at a common point called the vertex. Vertex Vertex: end point of the rays that form an angle. C A B

8. Degree: unit of measure. 95 0

9. Prerequisite Skills VOCABULARY CHECK Identify the object with the review word from the list: point, line, ray, plane, angle, vertex, degree. 2. 1. 3. ANSWER line ANSWER point ANSWER ray 4. A unit for measuring angles is a(n) ? . ANSWER degree

10. Classifying Angles Angles are classified by degrees. Acute - greater than 0 degrees but less than 90 degrees. C A B This is read “Angle ABC or Angle CBA, or just Angle B

11. Classifying Angles Obtuse – angles measuring more than 90 degrees but less than 180 degrees.

12. Classifying Angles Right Angles measure exactly 90 degrees and labeled with “square” in the corner of the angle.

13. Classifying Angles A straight angle “looks like” a straight line, but it actually is an angle. It measures exactly 180 degrees. A B C

14. Two angles are complementary if the sum of their measures is 90 degrees. 70 ° 20 ° 70 + 20 = 90 degrees.

15. Are these complementary angles? 60 ° 30 °

16. Two angles are supplementary if the sum of their measures is 180 degrees. 2

17. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 1. m 1 = 79 m 2 = 101 m 1+ m 2 = 79 ° + 101 ° ANSWER Hence, the angles are supplementary. = 180

18. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 2. m 1 = 64 m 1 = 36 m 1+ m 2 = 100 ° = 64 + 36 ANSWER Hence, 1 and 2 are neither complementary nor supplementary.

19. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 3. m 1 = 52 m 1 = 38 m 1+ m 2 = 52 + 38 = 90 ANSWER Hence, 1 and 2 are complementary.

20. Vertical Angles When two lines intersect at a point , they form two pairs of vertical angles. They do not share a side, and they have the same measure. 1 3 4 2 Angles 1 & 2 are vertical angles and 3&4 are vertical angles.

21. GUIDED PRACTICE for Example 2 Find the measures of the numbered angles. SOLUTION STEP 1 137° 43° 43° It is given that m 5 = 137 . 5 and 7 are vertical angles.Their measures are equal, so m 7 = 137 ° .

22. GUIDED PRACTICE for Example 2 Find the measures of the numbered angles. SOLUTION STEP 1 54° 126° 126° It is given that m 8 = 54 . 8 and 10 are vertical angles. Their measures are equal, so m 10 = 54 ° .

23. Homework Page 406 #1-11