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Understanding the Angle Addition Postulate

In this lesson, you'll explore the Angle Addition Postulate, which states that the sum of the measures of two smaller angles is equal to the measure of a larger angle formed by them. You will learn how to find the measures of angles and their bisectors through examples and engaging activities. By drawing and labeling angles, and applying the postulate, you'll gain a clearer understanding of the relationships between angles. Join us to enhance your geometry skills with practical applications of this fundamental concept!

nathan-mooney
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Understanding the Angle Addition Postulate

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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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