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1.3: Angles - Angles and segment addition postulate

Dive into the concepts of angle addition and segment addition postulates. Learn how to make and defend conjectures, construct geometric arguments, and apply theorems to solve problems involving angles and lines. This guide includes practical examples such as calculating angles and segment lengths using given relationships between points. Understand how to use the angle addition postulate to find missing angle measures and apply the segment addition postulate to determine distances between points on a line.

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1.3: Angles - Angles and segment addition postulate

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  1. 1.3: Angles- Angles and segment addition postulate GSE M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines

  2. Angle Addition Postulate • If R is in the interior of PQS, then m PQR + m RQS = m PQS. P R 30 20 Q S

  3. Find the m< CAB

  4. Example of Angle Addition Postulate 100 Ans: x+40 + 3x-20 = 8x-60 4x + 20 = 8x – 60 80 = 4x 20 = x 40 60 Angle PRQ = 20+40 = 60 Angle QRS = 3(20) -20 = 40 Angle PRS = 8 (20)-60 = 100

  5. Find the m< BYZ -2a+48 4a+9 4a+9

  6. Segment Addition Post. • If B is between A & C, then AB + BC = AC. C B A

  7. Write a mathematic equation for the diagram above using The segment addition postulate. What would the equation look like now?

  8. A flight from PVD to NY is 143 miles A flight from PVD to Washington DC is 355 miles A flight from NY to Washington DC is _____ miles

  9. Seg. Add. Post. Example • If J is between H and K and HJ=5x-3 , JK = 4x, HK = 8x, find HJ, JK, HK • Ans: Draw a diagram

  10. Example • M is between L and N. Find each measurement if: LM = 4x+6 , LN = 5x+10 MN = 3x – 4 LM + MN = LN LM =4(4)+6 = 22 MN = 3(4)-4 = 8 LN = 5(4)+10 = 30

  11. Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7

  12. Assignment

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