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Lesson 4 Angles and Angle Bisector • An angle is a figure formed by two rays with the same endpoint. The two rays are called the sides of the angle. The endpoint is called the vertex of the angle. Symbol for an angle is “” Vertex: B Sides: BA and BC A We use 3 letters when naming an angle. The vertex must be in the middle. The name of the angle to the left is B ABC C CBA B • Two angles are congruent angles if they have the same measures. Ex. 1 Name ALL the angles in the figure below. Would it be correct to name any of the angles Q? Explain. NO, because 3 of the angles have Q for a vertex. You need more information in the name to distinguish them from one another. It is always best to use 3 LETTERS to name an angle Angles are measured in units called degrees. To indicate the degree measure of an angle, write a lowercase m in front of the angle symbol. The degree measure of angle A is 80o. mA = 80o A protractor is used to find the measure of an angle. 1. Place the center of the protractor over the vertex. 2. Align the protractor with one side of the angle. 3. The second side of the angle crosses the protractor at So, mBAC = 65o o o Measure is between 0o and 90o Measure is between 90 and 180 When you see the small box, you know that the measure of the angle is 90. Measure is 90o Measure is 180o Angle Addition Theorem If you add two angles together, then they will share the vertex and the sum will create a larger angle. Ex 2. Find the measure PTM PTN + NTM = PTM Angle Add Theorem 37° + 43° =PTM PTM = 80° P N 37° 43° T M Ex 2. If ATD = x+21, Find the measure ATD ATN + NTD = ATD x+8 + x=1 x+12 =x+21 ATD = x+21 = (1)+21 = 22 Angle Add Theorem A N x+8 x+12 T D Reminder: when you see “arcs” on 2 angles, the angles are congruent. 110 An angle bisector is a ray (or a line segment) that divides an angle into two congruent angles. Its endpoint is at the vertex. BD bisects ABC A ABD DBC D B C Ex. 1 BD bisects ABC, and mABC = 110. Find mABD and mDBC. D A 110 B C mABD = mDBC Def of angle bisector = m ABC 2 = 110 2 = 55o MP bisects LMN and mLMP = 46 Ex. 2 L P 46 M mLMP = mPMN = 46o N a) Find mPMN and mLMN Def of angle bisector LMP +PMN = LMN Angle add thr mLMN = 2(46) = 92o b) Determine if LMN is acute, right, obtuse or straight. Obtuse Ex. 3 BD bisects ABC, mABD = (6x + 3)o, and mDBC = (8x – 7)o. Find mABD and mDBC. A (6x + 3)o D B (8x – 7)o C If an angle is ... Acute Right Obtuse Straight then the two angles formed by the bisector of the angle are both... acute acute acute right Class work • • • • • • • P 35 #1-3 P 38 #1-4, 9-10 P 37 # 4-6 P 39 # 24, 28 P 64 #2-12 (even) P 65 #18-20 P 66 # 28,30