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(over Lesson 3-2). 1-1a. Slide 1 of 2. (over Lesson 3-2). 1-1b. Slide 1 of 2. Vocabulary. §3.3 The Angle Addition Postulate. What You'll Learn. You will learn to find the measure of an angle and the bisector of an angle. NOTHING NEW!. R. X.

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1-1a

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  1. (over Lesson 3-2) 1-1a Slide 1 of 2

  2. (over Lesson 3-2) 1-1b Slide 1 of 2

  3. Vocabulary §3.3 The Angle Addition Postulate What You'll Learn You will learn to find the measure of an angle and the bisectorof an angle. NOTHING NEW!

  4. R X 2) Draw and label a point X in the interior of the angle. Then draw SX. S T §3.3 The Angle Addition Postulate 1) Draw an acute, an obtuse, or a right angle. Label the angle RST. 45° 75° 30° 3) For each angle, find mRSX, mXST, and RST.

  5. R X S T §3.3 The Angle Addition Postulate 1) How does the sum of mRSX and mXST compare to mRST ? Their sum is equal to the measure of RST . mXST = 30 + mRSX = 45 = mRST = 75 2) Make a conjecture about the relationship between the two smaller angles and the larger angle. 45° The sum of the measures of the twosmaller angles is equal to the measureof the larger angle. The Angle Addition Postulate (Video) 75° 30°

  6. P 1 Q A 2 R §3.3 The Angle Addition Postulate m1 + m2 = mPQR. There are two equations that can be derived using Postulate 3 – 3. m1 = mPQR –m2 These equations are true no matter where A is locatedin the interior of PQR. m2 = mPQR –m1

  7. X 1 Y W 2 Z §3.3 The Angle Addition Postulate Find m2 if mXYZ = 86 and m1 = 22. Postulate 3 – 3. m2 + m1 = mXYZ m2 = mXYZ –m1 m2 = 86 – 22 m2 = 64

  8. C D (5x – 6)° 2x° B A §3.3 The Angle Addition Postulate Find mABC and mCBD if mABD = 120. mABC + mCBD = mABD Postulate 3 – 3. Substitution 2x + (5x – 6) = 120 7x – 6 = 120 Combine like terms 7x = 126 Add 6 to both sides x = 18 Divide each side by 7 36 + 84 = 120 mCBD = 5x – 6 mABC = 2x mCBD = 5(18) – 6 mABC = 2(18) mCBD = 90 – 6 mABC = 36 mCBD = 84

  9. §3.3 The Angle Addition Postulate Just as every segment has a midpoint that bisects the segment, every angle has a ___ that bisects the angle. ray angle bisector This ray is called an ____________ .

  10. is the bisector of PQR. P 1 Q A 2 R §3.3 The Angle Addition Postulate m1 = m2

  11. Since bisects CAN, 1 = 2. N T 2 1 A C §3.3 The Angle Addition Postulate If bisects CAN and mCAN = 130, find 1 and 2. 1 + 2 = CAN Postulate 3 - 3 Replace CAN with 130 1 + 2 = 130 1 + 1 = 130 Replace 2 with 1 2(1) = 130 Combine like terms (1) = 65 Divide each side by 2 Since 1 = 2, 2 = 65

  12. End of Lesson

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