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

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

Find the m< CAB

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

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

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

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

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

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

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

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

Assignment