1. What’s Your Angle? SOL 8.6 Mr. Kozar Godwin Middle School

2. Unit Objectives Students will verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles and measure angles of less than 360 degrees.

3. Essential Questions How are vertical, adjacent, complementary and supplementary angles related? Adjacent angles are any 2 non-overlapping angles that share a common side and a common vertex. Vertical angles will always be nonadjacent angles. Supplementary and complementary angles may or may not be adjacent.

4. Essential Questions What are the relationships between the angles formed when 2 parallel lines are cut by a transversal? When 2 parallel lines are cut by a transversal, several pairs of angles are formed. Pairs of alternate interior angles, alternate exterior angles, and vertical angles are congruent. Adjacent angles, and same side (consecutive) interior angles are supplementary.

5. VOCABULARY

6. Types of lines Intersecting lines Parallel lines Perpendicular lines Lines that have 1 and only 1 point in common. When 2 lines intersect, 4 angles are formed. Lines in the same plane and never intersect. Same distance apart. Lines that intersect at right angles. 90 degrees

7. There are four main types of angles. Straight angle Right angle Acute angle Obtuse angle A B C A B C A B C BA C Types Of Angles

8. Protractor is used to measure and draw angles. Angles are accurately measured in degrees. Measurement Of An Angle

9. Right angle: An angle whose measure is 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

10. Obtuse angle: An angle whose measure is greater than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

11. Acute angle: An angle whose measure is less than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

12. Straight angle: An angle whose measure is 180 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

13. Pairs Of Angles : Types Adjacent angles Vertically opposite angles Complimentary angles Supplementary angles Linear pairs of angles Two angles that have a common vertex and a common ray Opposite angles Sum of two angles is 90 0 Sum of two angles is 180 0 Two adjacent supplementary angles

14. Two angles that have the same measure are called congruent angles. Congruent angles have the same size and shape. A B C 30 0 D E F D E F Congruent Angles

15. Adjacent Angles Two angles that have a common vertex and a common ray are called adjacent angles. C D B A Common ray Common vertex Adjacent Angles  ABD and  DBC Adjacent angles do not overlap each other. D E F A B C  ABC and  DEF are not adjacent angles

16. Non-Adjacent Angles Do NOT share a common side.

17. Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point.  APC =  BPD  APB =  CPD A D B C P Four angles are formed at the point of intersection. Point of intersection ‘P’ is the common vertex of the four angles. Vertically opposite angles are congruent.

18. If the sum of two angles is 90 0, then they are called complimentary angles. 60 0 A B C 30 0 D E F  ABC and  DEF are complimentary because 60 0 + 30 0 = 90 0  ABC +  DEF Complimentary Angles

19. If the sum of two angles is 180 0 then they are called supplementary angles.  PQR and  ABC are supplementary, because 100 0 + 80 0 = 180 0 R Q P A B C 100 0 80 0  PQR +  ABC Supplementary Angles

20. Transversal A line that intersects two or more coplanar lines in different points forming eight (8) angles. Interior angles lie between 2 lines

21. Alternate Interior Angles < 3 & < 6 < 4 & < 5 < 4 & < 6 < 3 & < 5 Same Side Interior Angles Alternate exterior lie outside the 2 lines < 1 <8 <2 <7

22. Reflex Angles Measure more than 180 degrees but less than 360 degrees.