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

R30 20

Find the m< CAB

Example of Angle Addition Postulate

Ans: x+40 + 3x-20 = 8x-60

4x + 20 = 8x – 60

80 = 4x

20 = x

Angle PRQ = 20+40 = 60

Angle QRS = 3(20) -20 = 40

Angle PRS = 8 (20)-60 = 100

60 40

100

4a+9

4a+9

-2a+48

Find the m< BYZ

Segment Addition Post.Segment Addition Post.• If B is between A & C, then

AB + BC = AC.

AA BBCC

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

4

82

10527

1054364

x

x

xx

xxx

LM + MN = LN

LM =4(4)+6 = 22

MN = 3(4)-4 = 8

LN = 5(4)+10 = 30

ExEx: if DE=2, EF=5, and : if DE=2, EF=5, and DE=FG, find FG, DF, DG, & DE=FG, find FG, DF, DG, &

EG.EG.DD EE

FFGG

FG=2FG=2

DF=7DF=7

DG=9DG=9

EG=7EG=7

Assignment