Lesson 6 - Angle Measure Notes PDF

Chapter 1 - Tools of Geometry Lesson 6 - Angle Measure and Angle Relationships Ray: part of a line consisting of ______ endpoint and all points to one side of the endpoint “Half” line How to name a RAY: 1. Use ________ points. a. First point listed MUST BE the ____...

Chapter 1 - Tools of Geometry Lesson 6 - Angle Measure and Angle Relationships Ray: part of a line consisting of ______ endpoint and all points to one side of the endpoint “Half” line How to name a RAY: 1. Use ________ points. a. First point listed MUST BE the _____________ b. Second point listed ANY OTHER ___________ on the ray 2. Place a ____________ ___________ ___________ above the ____________ points. Opposite Rays: two rays with the __________ endpoint, on the same line (collinear), extending in OPPOSITE directions, forming a straight line Example: ANGLE: formed by two (noncollinear) intersecting rays that have a common endpoint (vertex). Angle symbol: Sides Vertex Three ways to name an angle: Example 1: Refer to the below figure. _________a) Name the vertex of ∠1. _________b) Name the 2 sides of ∠4 _________c) Write another name for ∠TVW _________ _________ _________d) Write another name for ∠5 _________ Measuring an Angle: measured in units called ______________. 1 degree = 1/360th of a turn around a circle _______________ could be used to measure an angle Symbol for “measure of an angle” __________ Classifying angles: based on their measure Example: Acute: Right: Obtuse: Straight: Reflex: Example 2: Classify each angle as right, acute, or obtuse. Refer to the figure _________a) ∠NMP _________b) ∠OMN _________c) ∠NMQ ⃗⃗⃗⃗⃗⃗ and ______ are opposite rays _________d) MN Angle Addition/Subtraction Postulate Just like segments, angles can be divided into smaller parts and when those smaller parts are added together their sum equals the measure of the largest angle. Part + Part = Whole Whole – Part = Part Example 3: Find the measure of the angle. a) Find 𝑚∠LMN. b) Find 𝑚∠VTU.  c) If m∠RSU = 10x − 9, find m∠TSU. Congruent Angles: angles that have the _____________ degree measure Notation: Example Angle bisector: a ray that divides an angle into two congruent angles Example: Example 4: ⃗⃗⃗⃗⃗ bisects ∠𝑄𝑅𝑆. If the 𝑚∠𝑄𝑅𝑆 = 100°, then 𝑚∠𝑄𝑅𝑇 = ____________. a) 𝑅𝑇 Draw the figure. b) ⃗⃗⃗⃗⃗ 𝑌𝐴 bisects ∠𝑋𝑌𝑍. If the 𝑚∠𝑋𝑌𝐴 = 24°, then 𝑚∠𝑋𝑌𝑍 = ____________. Draw the figure. c) In the attached figure, ⃗⃗⃗⃗⃗ BD bisects ∠EBC. If m∠EBD = 4x + 16 and m∠DBC = 6𝑥 + 4, find m∠EBD.