3-3: The Angle Addition Postulate
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Transcript of 3-3: The Angle Addition Postulate
Angle Addition Postulate◦ For any angle PQR, if A is in the interior of PQR,
then mPQA + mAQR = mPQR
◦ What does it mean?1) Two small angles that share a side can be
added together to find their combined, larger angle.
2) If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle.
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A
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Q12
Angle Addition Postulate◦ For any angle PQR, if A is in the interior of PQR,
then mPQA + mAQR = mPQR
◦ What does it mean?1) Two small angles that share a side can be
added together to find their combined, larger angle.
2) If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle.
P
A
R
Q12
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 =
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A
R
Q12
64
This time, with some Algebra!◦ If ABD = 120, find ABC and CDB
◦ x = ◦ ABC = ◦ CDB =
183684
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˚
Assignment◦ Worksheet #3-3