WarmUp Billiards Pool Who has played pool Whats

Warm-Up: Billiards (“Pool”) • Who has played pool? • What’s a “bank shot”? • How do you know where to hit the ball on • the side? • It’s all in the angles! • Angles are the foundation of geometry

1. 4 Angles & their Measures Objectives: • Define: Angle, side, vertex, measure, degree, congruent • Name angles with the vertex always in the middle • Measure angles with a protractor • Identify congruent angles • Classify angles as acute, right, obtuse, or straight • Add and subtract angle measures using the angle addition postulate

Angle symbol: • 2 rays that share the same endpoint (or initial point) Sides – the rays XY & XZ Y 5 X Z Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Vertex – the common endpoint; X Angles can also be named by a #. (<5)

In the figure, there are three different <Q’s (two smaller ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

Example 1: Naming Angles One angle only: < EFG or < GFE Three angles: < ABC or < CBA < CBD or < DBC < ABD or < DBA

Angle Measurement

Postulate 3: Protractor Post. • The rays of an angle can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s. 55 o 20 o m<A = 55 -20 = 35 o

Interior or Exterior? • B is ______ in the interior • C is ______ in the exterior on the < • D is ______ B C A D

Adjacent Angles • 2 angles that share a common vertex & side, but have no common interior parts. (they have the same vertex, but don’t overlap) such as <1 & <2 2 1

Postulate 4: Angle Addition Postulate

Example 2: m < FJH = m < FJG + m < GJH m < FJH = 35° + 60°

Example 3: . S P If m<QRP=5 xo, m<PRS=2 xo, & m<QRS=84 o, find x. 5 x+2 x=84 Q 7 x=84 x=12 m<QRP=60 o m<PRS=24 o R

Types of Angles • Acute angle – Measures between 0 o & 90 o • Right angle – Measures exactly 90 o • Obtuse angle – Measures between 90 o & 180 o • Straight angle –Measures exactly 180 o

Example 4: Classifying Angles • A. straight • B. acute • C. obtuse

Example 5: • Name an acute angle <3, <2, <SBT, or <TBC • Name an obtuse angle <ABT • Name a right angle <1, <ABS, or <SBC • Name a straight angle <ABC S T 3 1 A 2 B C

Assignment General 1. 4 A Honors 1. 4 B