Geometry 916 2 1 1 Angle Relationships 2

Geometry 9/16 2. 1. 1 : Angle Relationships

2. 1. 1: Angle Relationships • To understand relationships of angles, you need to be able to name and refer to specific angles. • Using ΔABC: • The top is called “angle A”, written mathematically as ∠A • Point A is called a vertex of ΔABC. • If ΔABC is equilateral, write an equation to show the relationship of its angles. m∠A = m∠B = m∠C

• Rotate ΔABC to create ΔAB’C’: • If I say “the angles at A are equal”, what do I mean? • How many angles are at Pt. A? Are there more than 3? Yes – There are 6! • Be specific when describing all the two equal angles I mentioned. • One of the angles is ∠BAB’. What’s the other? ∠CAC’ • When two angles are equal, they are called CONGRUENT ∠’S • Be sure to use 3 letters when describing a specific angle • Especially if there is more than one angle in that location!

Angle Relationships • Two angles whose measures have a sum of 90° are called complementary angles. ∠ABC and ∠CBD are complementary. If m∠CBD = 76°, what is m∠ABC? m∠ABC = 14 o • If the sum of the measures of two angles is 180°, they are called supplementary angles. ∠LMN is a straight angle m∠LMP + m∠NMP = 180 o, so ∠LMP & ∠NMP are supplementary. If m∠LMP = 62°, what is m∠PMN? m∠PMN = 118 o

• Now consider the diagram below, which shows and intersecting at E. • If x = 23°, find m∠AEC, m∠DEB, and m∠CEB. Show all work. m∠AEC = 157 o m∠DEB = 157 o m∠CEB = 23 o • Which angles are the same? Write in equations to show the relationships. m∠AEC = m∠DEB m∠AED = m∠CEB • When two lines intersect, the angles that lie on opposite sides of the intersection point are called vertical angles. • Which angle pairs are vertical angles in the above diagram? ∠AEC & ∠DEB ∠AED & ∠CEB

Practice!! • Work on Problem 2 -5 in your textbook. Use the notes you just took on angle relationships! • HOMEWORK: Ch. 2 (8 -12) – DUE Fri 9/18