1.3: Angles - Angles and segment addition postulate

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