1. ANGLES

2. To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. For example:  ABC or  CBA We may also name this angle only by the single letter of the vertex, for example  B. A B C Naming An Angle

3. There are four main types of angles. Straight angle 180 o Right angle 90 o Acute angle Less than 90 o Obtuse angle More than 90 o A B C A B C A B C BA C Types Of Angles

4. A B C D E F P Q R Which of the angles below is a right angle, acute angle and an acute angle? Right angle Obtuse angle Acute angle 1. 2. 3.

5. 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

6. 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.

7. 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 Vertically opposite angles are congruent.

8. 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

9. 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

10. A line that intersects two or more lines at different points is called a transversal. (transversal) B A D C P Q G F Pairs Of Angles Formed by a Transversal Eight angles are formed in all by the transversal.

11. Corresponding Angles A transversal creates pairs of corresponding angles. (angles in the same spot in both lines) Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.  GPB =  PQE  GPA =  PQD  BPQ =  EQF  APQ =  DQF Line M B A Line N D E L P Q G F Line L

12. Alternate Interior Angles Alternate interior angles are formed on opposite sides of the transversal on the inside of the lines. Line M B A Line N D E L P Q G F Line L  BPQ =  DQP  APQ =  EQP Pairs of alternate interior angles are congruent.

13. Alternate Exterior Angles Alternate exterior angles are formed on opposite sides of the transversal and on the outside of the lines. B A D E L P Q G F  BPG =  DQF  APG =  EQF Pairs of alternate exterior angles are congruent.

14. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called same side interior angles. A pair of interior angles lie on the same side of the transversal. The measures of interior angles in each pair add up to 180 0. Same Side Interior Angles Line M B A Line N D E L P Q G F Line L 60 0 120 0 60 0  BPQ +  EQP = 180 0  APQ +  DQP = 180 0

15. The angles that lie in the area outside the two parallel lines that are cut by a transversal, are called same side exterior angles. The measures of exterior angles in each pair add up to 180 0. Same Side Exterior Angles Line M B A Line N D E L P Q G F Line L 60 0 120 0 60 0  BPG +  EQF = 180 0  APG +  DQF = 180 0

16. Angles in a Triangle All angles in a triangle will add up to 180 o = 60 o = 80 o

17. Name the pairs of the following angles formed by a transversal. Line M B A Line N DE P Q G F Line L Line M B A Line N D E P Q G F Line L Line M B A Line N D E P Q G F Line L 50 0 130 0