Section 1.4 Angles and Their Measures standards #4 & 12 Monday, November 14, 2016

Goals Use angle postulates Classifying Angles

ANGLE Consists of two different rays that have the same initial point. The rays are the sides of the angle and the initial point is the vertex of the angle. A B C <ABC <CBA BA & BC are the rays, which make up the sides. Names : & Vertex- the middle letter when naming an angle & <B

Exterior/Interior Point(s) w Interior Interior of an angle: within the sides of an angle. Exterior of an angle: not on or within the angle. Exterior

Protractor A protractor is used to measure an angle. The measure that is found can be approximated with units called degrees. The symbol for degrees : °

Classifying Angles A m<A < 90° 1) Acute Angle

2) Right Angle A m<A = 90°

3) Obtuse Angle A m<A: between 90° and 180°

4) Straight Angle A m<A = 180°

Adjacent Angles Two angles that share a common vertex and side, but have no common interior points. R S T P  RSP and  TSP are adjacent, SP is the common side and S is the common vertex.

Angle Addition Postulate If P is in the interior of  RST, then m  RSP + m  TSP = m  RST R S T P m  RSP m  TSP

Example #1 Name & classify the angles in the figure.    M N O P 1) <MNP or <PNM, Acute 2) <PNO or <ONP, Obtuse 3) <ONM or <MNO, Straight

Example #2 R S T P The m<RST = 115° and the m<RSP = 75°. Find the m<TSP and then classify the angle… ? 75° 115° 1) m<RSP + m<TSP = m<RST 2) 75° + x° = 115° 3) m<TSP = 40°, acute

Example #3 S T P Name the vertex and sides of the angle. Then estimate & classify its measure. 1) Vertex: S 2) Sides: SP & ST 3) Estimated measure: 60°, acute

Example #4 Use a straightedge to draw two adjacent angles  LMN and  NMO so that  LMN is acute and  LMO is straight. L N M O

Assignment 1.4 HW Page 29 # (e)