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The Angle Addition Postulate

Vocabulary. 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. S. T. The Angle Addition Postulate. 1) Draw an acute, an obtuse, or a right angle. Label the angle RST. R.

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The Angle Addition Postulate

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  1. Vocabulary 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!

  2. R S T The Angle Addition Postulate 1) Draw an acute, an obtuse, or a right angle. Label the angle RST.

  3. R X 2) Draw and label a point X in the interior of the angle. Then draw SX. S T The Angle Addition Postulate 1) Draw an acute, an obtuse, or a right angle. Label the angle RST.

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

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

  6. R X 2) Draw and label a point X in the interior of the angle. Then draw SX. S T 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.

  7. R X S T The Angle Addition Postulate 1) How does the sum of mRSX and mXST compare to mRST ? 45° 75° 30°

  8. R X S T 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 45° 75° 30°

  9. R X S T 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° 75° 30°

  10. R X S T 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. 75° 30°

  11. P 1 Q A 2 R The Angle Addition Postulate

  12. P 1 Q A 2 R The Angle Addition Postulate m1 + m2 = mPQR.

  13. P 1 Q A 2 R The Angle Addition Postulate m1 + m2 = mPQR. There are two equations that can be derived using Postulate 3 – 3.

  14. P 1 Q A 2 R 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 m2 = mPQR –m1

  15. P 1 Q A 2 R 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

  16. X 1 Y W 2 Z The Angle Addition Postulate Find m2 if mXYZ = 86 and m1 = 22.

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

  18. X 1 Y W 2 Z 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

  19. X 1 Y W 2 Z 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

  20. X 1 Y W 2 Z 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

  21. C D (5x – 6)° 2x° B A The Angle Addition Postulate Find mABC and mCBD if mABD = 120.

  22. C D (5x – 6)° 2x° B A The Angle Addition Postulate Find mABC and mCBD if mABD = 120. mABC + mCBD = mABD Postulate 3 – 3.

  23. C D (5x – 6)° 2x° B A 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

  24. C D (5x – 6)° 2x° B A 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

  25. C D (5x – 6)° 2x° B A 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

  26. C D (5x – 6)° 2x° B A 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

  27. C D (5x – 6)° 2x° B A 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 mABC = 2x mABC = 2(18) mABC = 36

  28. C D (5x – 6)° 2x° B A 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 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

  29. C D (5x – 6)° 2x° B A 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

  30. The Angle Addition Postulate Just as every segment has a midpoint that bisects the segment, every angle has a ___ that bisects the angle.

  31. The Angle Addition Postulate Just as every segment has a midpoint that bisects the segment, every angle has a ___ that bisects the angle. ray

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

  33. 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 ____________ .

  34. 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 ____________ .

  35. P 1 Q A 2 R The Angle Addition Postulate

  36. is the bisector of PQR. P 1 Q A 2 R The Angle Addition Postulate

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

  38. N T 2 1 A C The Angle Addition Postulate If bisects CAN and mCAN = 130, find 1 and 2.

  39. Since bisects CAN, 1 = 2. N T 2 1 A C The Angle Addition Postulate If bisects CAN and mCAN = 130, find 1 and 2.

  40. Since bisects CAN, 1 = 2. N T 2 1 A C The Angle Addition Postulate If bisects CAN and mCAN = 130, find 1 and 2. 1 + 2 = CAN Postulate 3 - 3

  41. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  42. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  43. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  44. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  45. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  46. Since bisects CAN, 1 = 2. N T 2 1 A C 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

  47. The Angle Addition Postulate End of Lesson

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