1-5 Angle Relationships What are: adjacent angles linear pairs vertical angles complementary angles supplementary angles perpendicular lines

Adjacent angles Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points. 1 2  

Linear Pair A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays. 1 2  

Definition Two angles, , form a linear pair if and only if A, B, and C are collinear and D is not on . A B C D

Name all the linear pairs F G H K J

Vertical Angles Two angles are vertical angles if and only if their sides form two pairs of opposite rays. OR…When two lines intersect, they form two pairs of vertical angles. 2 1 3 4

Definition Complementary angles are two angles whose measures add up to 90° A B C D

Try it Find the measures of 1 2 3 134°

Definition Supplementary angles are two angles whose measures add up to 180° R S T U

Linear Pair Postulate The angles in a linear pair are supplementary

What is the difference? Supplementary because it adds to 180° AND Linear pair because both angles are on the same line.

Complementary or Supplementary? 41° 49° 41° 139° P S Angles can be complementary or supplementary regardless of their location.

find the measures of the angles that are complementary and supplementary to 90°− 64° = 26° Supplementary 180°− 64° = 116°

Review

Review

Assignment 1-5 Page 51, 8-17, 25-28

Angle Relationships Day 2 What are perpendicular lines? What can be assumed or not assumed in a drawing?

Perpendicular Lines Lines, line segments or rays that form right angles are perpendicular. B A D C

B Perpendicular Lines A C   D

To Assume or Not to Assume… In the figure, do you think you would be justified in assuming that: B, C, and E are collinear? A B C E F G BE ll GD? D

Make a List… Make a list of rules about what you think you can and cannot assume. A B C E F G

What can and cannot be assumed You May Assume: You May Not Assume (unless marked): Things that look straight are straight. Exact measurements and relative sizes of figures. Points shown on a line are collinear. All points shown are coplanar. Parallel or perpendicular lines. Relative position of points are accurate (intersection, between-ness). Congruence

To Assume or Not to Assume… Point S is between R and T. Points R,S, and T are collinear. Point S is the midpoint of RT. VY<TY R S T V W Y Z

Assignment 1-5 Day 2 p. 52, 36-41 And worksheet 1-5