Geometry Lesson 1 5 Angle Relationships Objective Identify

Geometry Lesson 1 – 5 Angle Relationships Objective: Identify and use special pairs of angles. Identify perpendicular lines.

Adjacent angles 2 angles that lie in the same plane and have a common vertex and side, but no common interior points.

Determine whether angles 1 and 2 are adjacent. No, do not share a common side Yes No, angles do not share a vertex or side.

Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. No, angles do not share a vertex.

Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. Yes No, angles do not Share a vertex.

Determine whether the pair of angles are adjacent. A B C E D Yes No, can’t have one angle inside the other.

Linear Pair A pair of adjacent angles with noncommon sides that are opposite rays. Linear pairs are supplementary

Example In the figure, CM and CE are opposite rays. Name the angle that forms a linear pair with angle 1 *Hint: what completes the 180 degrees or straight line Do form a linear pair? Justify your answer. No, they do not form a linear pair. The two angles do not add up to be 180 and do not create opposite rays.

Your turn Name the angle that forms a linear pair with Tell whether form a linear pair. Justify your answer. Yes, they are adjacent and their noncommon sides are opposite rays.

Your Turn Name the angle that forms a linear pair with Do Justify your answer. form a liner pair? No, they are not adjacent angles.

Vertical Angles Vertical angle: l Two angles are vertical if and only if they are two nonadjacent angles formed by a pair of interesting lines. 100 80 80 100

Theorem Vertical angle Theorem: l Vertical angles are congruent.

Example Find the value of x in each figure. x = 130 (vertical) 5 x = 25 x=5

Complementary Angles 2 angles with measures that have a sum of 90.

Supplementary Two angles with measures that have a sum of 180.

Example Find the measure of two supplementary angles if the difference in the measures of the two angles is 18. Let one angle be x and the other y. + Write your equations. x – y = 18 99 + y = 180 x + y = 180 2 x = 198 x = 99 y = 81

Example Find the measure of 2 complementary angles if the measure of the larger angle is 12 more than twice the measure of the smaller angle. Let x and y be the angles x = 12 + 2 y x + y = 90 (12 + 2 y) + y = 90 3 y + 12 = 90 3 y = 78 y = 26 x = 12 + 2(26) = 64

Perpendicular Lines Form 4 right angles Form congruent adjacent angles Segments and rays can be perpendicular Right angle symbol shows perpendicular.

Example Find x and y so that PR and SQ are perpendicular. 2 x + 5 x + 6 = 90 7 x = 84 x = 12 4 y – 2 = 90 4 y = 92 y = 23

Interpreting Diagrams Are the lines perpendicular?

Interpret What can you assume? What appears true, but cannot be assumed?

Determine whether each statement can be assumed from the figure. Explain. are complementary No, congruent but we don’t know if complementary are a linear pair. Yes, adjacent angles whose noncommon sides are opposite rays Yes, they form a right angle which means they are perpendicular.

Homework Pg. 50 1 – 7 all, 8 – 44 EOE, 58 – 66 E