Pairs of Angles

Pairs of Angles

1. Pairs of Angles : Types Adjacent angles Vertically opposite angles Complementary angles Supplementary angles Linear pairs of angles NM Spirit

2. 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 NM Spirit

3. Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. Ð APC = Ð BPD Ð APB = Ð 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. NM Spirit

4. If the sum of two angles is 90 , then they are called complementary angles. 60 A B C 30 D E F Ð ABC and Ð DEF are complementary because 60 + 30 = 90 Ð ABC + Ð DEF Complementary Angles NM Spirit

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

6. Two adjacent supplementary angles are called linear pair of angles. A 60 120 P C D 60 + 120 = 180 Ð APC + Ð APD Linear Pair Of Angles NM Spirit

7. A line that intersects two or more lines at different points is called a transversal . Line L (transversal) B A Line M Line N D C P Q G F Pairs Of Angles Formed by a Transversal Line M and line N are parallel lines. Line L intersects line M and line N at point P and Q. Four angles are formed at point P and another four at point Q by the transversal L. Eight angles are formed in all by the transversal L. NM Spirit

8. Pairs Of Angles Formed by a Transversal Corresponding angles Alternate angles Interior angles NM Spirit

9. Corresponding Angles When two parallel lines are cut by a transversal , pairs of corresponding angles are formed. Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent . Ð GPB = Ð PQE Ð GPA = Ð PQD Ð BPQ = Ð EQF Ð APQ = Ð DQF Line M B A Line N D E L P Q G F Line L NM Spirit

10. Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points . Line M B A Line N D E L P Q G F Line L Ð BPQ = Ð DQP Ð APQ = Ð EQP Pairs of alternate angles are congruent . Two pairs of alternate angles are formed. NM Spirit

11. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called 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 . Interior Angles Line M B A Line N D E L P Q G F Line L 60 120 120 60 Ð BPQ + Ð EQP = 180 Ð APQ + Ð DQP = 180 NM Spirit