Angle Relationships Section 1-5

Adjacent angles are angles that: C) Have no interior points in common Definition of Adjacent Angles Adjacent angles are angles that: A) Share a common side B) Have the same vertex C) Have no interior points in common

Determine whether 1 and 2 are adjacent angles. No: They have a common vertex B, but _____________ 1 2 B no common side Yes have the same vertex G and a common side with no interior points in common. 1 2 G N 1 2 J L No: They do not have a common vertex or ____________ a common side

Complementary Angles Definition of Complementary Angles E A D 60° 30°   60° D E F 30° A B C  

ABC is the complement of DEF and DEF is the complement of ABC. Complementary Angles If two angles are complementary, each angle is a complement of the other. ABC is the complement of DEF and DEF is the complement of ABC. 60° D E F 30° A B C Complementary angles DO NOT need to have a common side or even the same vertex.

Some examples of complementary angles are shown below. 75° I   15° H 50° H 40° Q P S   30° 60° T U V W Z  

Supplementary Angles Definition of Supplementary Angles D C 130° 50° B   130° D E F 50° A B C  

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

 I is the supplement of  H and  H is the supplement of  I. Supplementary Angles If two angles are supplementary, each angle is a supplement of the other.  I is the supplement of  H and  H is the supplement of  I. 75° I 105° H Supplementary angles DO NOT need to have a common side or even the same vertex.

Some examples of supplementary angles are shown below. 105° H 75° I   50° H 130° Q P S   60° 120° T U V W Z   and  

Linear Pairs of Angles Definition of Linear Pairs Two angles form a linear pair if and only if (iff): A) They are adjacent B) Their non-common sides are opposite rays C A D B 1 2 A Linear Pair is a set of Supplementary/Adjacent Angles

Linear Pairs of Angles In the figure, and are opposite rays. 1 2 M 4 3 E H T A C 1) Name the angle that forms a linear pair with 1. ACE ACE and 1 have a common side the same vertex C, and opposite rays and 2) Do 3 and TCM form a linear pair? Justify your answer. No. Their noncommon sides are not opposite rays.

Two angles are vertical iff : Vertical Angles Definition of Vertical Angles Two angles are vertical iff : they are two non-adjacent angles formed by a pair of intersecting lines. Vertical angles: 1 and 3 1 4 2 2 and 4 3

Vertical Angles Vertical angles are congruent. Theorem: Vertical Angle 2 1  3 3 1 2  4 4

Vertical Angles Find the value of x in the figure: (x – 10) = 125. 125° x = 135.

Supplementary angles   B C G A D F E

Complementary angles   E F D C G J H

Perpendicular lines special intersecting lines that form right angles Perpendicular lines intersect to form 4 right angles.

Congruent Angles Definition of Congruent Two angles are congruent iff, they have the same ______________. degree measure B  V iff 50° V mB = mV 50° B

HOMEWORK Pg. 50-54 #1-26, 29-32 36-41