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Ch 2 Sect 2. Angle Bisectors. An angle bisector is a ray that divides an angle into two smaller congruent angles. (cuts it in half).
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Ch 2 Sect 2 Angle Bisectors An angle bisector is a ray that divides an angle into two smaller congruent angles. (cuts it in half) Look for markings to indicate that an angle has been bisected. When working problems, make marks on quizzes and tests to remember where the two congruent angles are located. Keep these relationships in mind when working with bisectors: Left + Right = Whole Left = Right Whole = small 2 (small) = whole 2
Example 1 SOLUTION mABD BDbisects ABC. = Simplify. ANSWER Find Angle Measures BD bisectsABC, andmABC = 110°. Find mABDandmDBC. 1 1 2 2 (mABC) Substitute110°formABC. = (110°) = 55° ABD andDBCare congruent, somDBC= mABD. So,mABD = 55°, andmDBC = 55°.
Checkpoint HK bisectsGHJ. FindmGHKandmKHJ. ANSWER ANSWER ANSWER 26°; 26° 80.5°; 80.5° 45°; 45° Find Angle Measures 1. 2. 3.
Example 2 MP bisectsLMN, andmLMP =46°. b. Determine whether LMN is acute, right, obtuse, or straight. Explain. SOLUTION a. MP bisectsLMN, somLMP = mPMN . b. LMN is obtuse because its measure is between 90° and 180°. Find Angle Measures and Classify an Angle a. Find mPMNandmLMN. You know thatmLMP = 46°. Therefore, mPMN = 46°. The measure ofLMN is twice the measure of LMP. mLMN =2(mLMP) = 2(46°) = 92° So, mPMN = 46°, andmLMN = 92°
Checkpoint QSbisectsPQR.FindmSQPandmPQR. Then determine whether PQRis acute, right, obtuse, or straight. ANSWER ANSWER 29°; 58°; acute 45°; 90°; right ANSWER 60°; 120°; obtuse Find Angle Measures and Classify an Angle 4. 5. 6.
Example 3 SOLUTION mDAB = 2(mABC) ACbisects DAB. Substitute45°formBAC. mBCD = CAbisects BCD. Use Angle Bisectors In the kite, DABis bisected AC,and BCDis bisected by CA.Find mDABandmBCD. 2(mACB) Simplify. 2(45°) = = 2(27°) = = 90° 54° Substitute27°formACB. Simplify. The measure of DABis 90°, and the measure ofBCDis 54°. ANSWER
Checkpoint 7. KM bisectsJKL. FindmJKMandmMKL. ANSWER ANSWER 48°; 48° 60°; 120° 8. UVbisectsWUT. FindmWUVandmWUT. Use Angle Bisectors
Example 4 RQ bisects PRS.Find the value of x. RQbisects PRS. Use Algebra with Angle Measures SOLUTION mQRS Substitute givenmeasures. (6x + 1)° Subtract 1 from each side. mPRQ = 6x = 84 6x + 1 – 1 Simplify. 85° = Divide each side by 6. = 85 – 1 6x 84 –– –– Simplify. x = 14 = 6 6 CHECK You can check your answer by substituting 14 for x. mPRQ = (6x + 1)° = (6 · 14 + 1)° = (84 + 1)° = 85°
Checkpoint BD bisectsABC.Find the value of x. ANSWER ANSWER 43 3 Use Algebra with Angle Measures 9. 10.
Ch 2 Sect 2 Homework: page 64-66 #1-22, 28-30