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Ch 2 Sect 2

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

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  1. 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

  2. Example 1 SOLUTION mABD BDbisects ABC. = Simplify. ANSWER Find Angle Measures BD bisectsABC, andmABC = 110°. Find mABDandmDBC. 1 1 2 2 (mABC) Substitute110°formABC. = (110°) = 55° ABD andDBCare congruent, somDBC= mABD. So,mABD = 55°, andmDBC = 55°.

  3. Checkpoint HK bisectsGHJ. FindmGHKandmKHJ. ANSWER ANSWER ANSWER 26°; 26° 80.5°; 80.5° 45°; 45° Find Angle Measures 1. 2. 3.

  4. Example 2 MP bisectsLMN, andmLMP =46°. b. Determine whether LMN is acute, right, obtuse, or straight. Explain. SOLUTION a. MP bisectsLMN, somLMP = mPMN . b. LMN is obtuse because its measure is between 90° and 180°. Find Angle Measures and Classify an Angle a. Find mPMNandmLMN. You know thatmLMP = 46°. Therefore, mPMN = 46°. The measure ofLMN is twice the measure of LMP. mLMN =2(mLMP) = 2(46°) = 92° So, mPMN = 46°, andmLMN = 92°

  5. Checkpoint QSbisectsPQR.FindmSQPandmPQR. 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.

  6. Example 3 SOLUTION mDAB = 2(mABC) ACbisects DAB. Substitute45°formBAC. mBCD = CAbisects BCD. Use Angle Bisectors In the kite, DABis bisected AC,and BCDis bisected by CA.Find mDABandmBCD. 2(mACB) Simplify. 2(45°) = = 2(27°) = = 90° 54° Substitute27°formACB. Simplify. The measure of DABis 90°, and the measure ofBCDis 54°. ANSWER

  7. Checkpoint 7. KM bisectsJKL. FindmJKMandmMKL. ANSWER ANSWER 48°; 48° 60°; 120° 8. UVbisectsWUT. FindmWUVandmWUT. Use Angle Bisectors

  8. Example 4 RQ bisects PRS.Find the value of x. RQbisects PRS. Use Algebra with Angle Measures SOLUTION mQRS Substitute givenmeasures. (6x + 1)° Subtract 1 from each side. mPRQ = 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. mPRQ = (6x + 1)° = (6 · 14 + 1)° = (84 + 1)° = 85°

  9. Checkpoint BD bisectsABC.Find the value of x. ANSWER ANSWER 43 3 Use Algebra with Angle Measures 9. 10.

  10. Ch 2 Sect 2 Homework: page 64-66 #1-22, 28-30

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