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3-3: The Angle Addition Postulate

3-3: The Angle Addition Postulate. 3-3: The Angle Addition Postulate. Angle Addition Postulate For any angle PQR, if A is in the interior of PQR, then m PQA + m AQR = m PQR What does it mean?

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3-3: The Angle Addition Postulate

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  1. 3-3: The Angle Addition Postulate

  2. 3-3: The Angle Addition Postulate • Angle Addition Postulate • For any angle PQR, if A is in the interior of PQR, then mPQA + mAQR = mPQR • What does it mean? • Two small angles that share a side can be added together to find their combined, larger angle. • If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle. P A 1 Q 2 R

  3. 3-3: The Angle Addition Postulate • Angle Addition Postulate • For any angle PQR, if A is in the interior of PQR, then mPQA + mAQR = mPQR • What does it mean? • Two small angles that share a side can be added together to find their combined, larger angle. • If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle. P A 1 Q 2 R

  4. 3-3: The Angle Addition Postulate • Examples • If PQA = 35 and AQR = 40, find PQR • PQR = PQA + AQR • PQR = 35 + 40 substitute • PQR = 75 • If PQR = 86 and AQR = 22, find PQA • PQA = P A 1 Q 64 2 R

  5. 3-3: The Angle Addition Postulate • This time, with some Algebra! • If ABD = 120, find ABC and CDB • x = • ABC = • CDB = 18 36 84

  6. 3-3: The Angle Addition Postulate • Just like every segment has a midpoint, every angle has a ray that bisects the angle. This ray is called the ANGLE BISECTOR. • If AT bisects CAN and CAN = 130, find 1 & 2. • Since AT bisects, 1 = 2 • CAN = 1 + 2 Angle Addition Postulate • 130 = 1 + 1 Substitution • 130 = 2  1 Combine • 65 = 1 Divide both sides by 2 • 1 and 2 both are 65˚

  7. 3-3: The Angle Addition Postulate • Assignment • Worksheet #3-3

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