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

Angles can also be named by a #. (<5) Angle symbol: 2 rays that share the same endpoint (or initial point) Sides – the rays XY & XZ Vertex – the common endpoint; X Y X 5 Z Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). 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: Three angles: < EFG or < GFE < 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. 55o 20o m<A = 55-20 = 35o

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

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

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

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

<3, <2, <SBT, or <TBC <1, <ABS, or <SBC 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 2 A B C

Assignment General 1.4 A Honors 1.4 B