Pairs of Angles
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This document defines and describes different types of angles: 1) Adjacent angles share a common vertex and side. Vertically opposite angles are formed when two lines intersect and are equal. 2) Complementary angles have a sum of 90 degrees. Supplementary angles have a sum of 180 degrees. 3) A linear pair is two adjacent supplementary angles. 4) A transversal intersects two or more lines. It forms corresponding, alternate, and interior angles that follow specific properties.
Pairs of Angles
- 1. Pairs of Angles : Types• Adjacent angles • Vertically opposite angles • Complementary angles • Supplementary angles • Linear pairs of angles
- 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
- 3. Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. APC = BPD APB = CPD A DB 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.
- 4. If the sum of two angles is 900, then they are called complementary angles. 600 A B C 300 D E F ABC and DEF are complementary because 600 + 300 = 900 ABC + DEF Complementary Angles
- 5. If the sum of two angles is 1800 then they are called supplementary angles. PQR and ABC are supplementary, because 1000 + 800 = 1800 RQ P A B C 1000 800 PQR + ABC Supplementary Angles
- 6. Two adjacent supplementary angles are called linear pair of angles. A 600 1200 PC D 600 + 1200 = 1800 APC + APD Linear Pair Of Angles
- 7. A line that intersects two or more lines at different points is called a transversal. Line L (transversal) BA Line M Line N DC 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.
- 8. Pairs Of Angles Formed by a Transversal • Corresponding angles • Alternate angles • Interior angles
- 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. GPB = PQE GPA = PQD BPQ = EQF APQ = DQF Line M BA Line N D E L P Q G F Line L
- 10. Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M BA Line N D E L P Q G F Line L BPQ = DQP APQ = EQP Pairs of alternate angles are congruent. Two pairs of alternate angles are formed.
- 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 1800. Interior Angles Line M BA Line N D E L P Q G F Line L 600 1200 1200 600 BPQ + EQP = 1800 APQ + DQP = 1800