4-7 Vertical Angles

Vertical angle definition Two angles are vertical angles if their sides form two pairs of opposite rays.  1 and  2 are vertical angles

Vertical angle theorem Vertical angles are congruent Create a sketch Write the given and the prove Given:  1 and  2 are a vertical angles Prove:  1   2

Vertical angle theorem Vertical angles are congruent StatementsReasons 1.  1 and  2 are vertical angles Given 2.Def of vertical angles 3.  1 and  3 form a linear pair  2 and  3 form a linear pair Def of linear pair 4.  1 is supplementary to  3  2 is supplementary to  3 Supplement Postulate 5.  3   3 Reflexive prop 6.  1   2 Supplement Theorem Q.E.D.

Perpendicular Lines theorem If 2 lines are perpendicular they form four right angles Create a sketch Write the given and the prove Given: L 1  L 2 Prove:  1,  2,  3,  4 are right angles L2L2 L1L1

Perpendicular Lines theorem If 2 lines are perpendicular they form four right angles StatementsReasons 1. L 1  L 2 Given 2.  1 is a right angle Def of perpendicular 3.m  1 = 90 Def. of right angle 4.  1 and  2 are a linear pair Given sketch 5.  1 and  2 are a supplementary Supplement Postulate 6.m  1 + m  2 = 180 Def of suppl m  2 = 180 Substitution 2 into 6 8.m  2 = 90 Subtraction prop. of eq. 9.m  3 = 90 Vertical Angle Theorem 10.m  4 = m  90 Vertical Angle Theorem Q.E.D.

Homework Pg. 106 – 108: # In 10, note that the problem is discussing two situations. Pg. 109 #1, 2