1. Unit 1 Foundations of Geometry Segments and Rays
Post : Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. A B C
G is between F and H, FG = 6, and FH = 11. Find GH.
Draw a diagram representing the situation. F G H 6 11
FH = FG + GH
Seg. Add. Postulate
11 = 6 + GH
Substitute 6 for FG and 11 for FH.

2. Unit 1 Foundations of Geometry Segments and Rays
Mr. Mack’s happy home
The distance from Mr. Mack’s house to the Mellow Mushroom is 12 miles.
If Mr. Rick’s house is the midpoint between Mellow Mushroom and Mr. Mack’s house, how far does Mr. Mack live from Mr. Rick?
Mr. Rick’s house
Mellow Mushroom

3. Unit 1 Foundations of Geometry Segments and Rays
Midpoint: a point that divides a segments into
two congruent segments. We say point B bisects segment AC A B C
If AB = 25, find the value of AN and NB.
M is the midpoint of RT. Find RM, MT, and RT.

4. Unit 1 Foundations of Geometry Angles
Angle: is formed by two rays with the same endpoint.
The rays are the sides of the angles.
The endpoint is the vertex of the angle. B T Q 1
The sides of the angle are BQ and BT.
The vertex is B.
The angle can be named: B, TBQ, QBT, and 1. A C B D E
Which is angle A?

5. Unit 1 Foundations of Geometry Angles
Special Angles x
right angle
x = 90 x
obtuse angle
90<x<180 x
acute angle
0<x<90 x
straight angle
x = 180

6. Unit 1 Foundations of Geometry Angles
Post. 1-8: Angle Addition Postulate
If point B is in the interior of AOC, then
mAOB + mBOC = mAOC.
If AOC is a straight angle, then mAOB + mBOC = 180. A B C O
m1+m2 = mAOC A B C O 1 2 1 2
m1+m2 = 180
mDEG = 115°, and F is in interior of DEG. Find mFEG if mDEF = 48°.

7. Unit 1 Foundations of Geometry Angles
An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects LJM; thus LJK  KJM.
KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

8. Unit 1 Foundations of Geometry Angles
KM bisects JKL, mJKM = (2x + 9)°, and mJKL = (6x – 10)°. Find mLKM.

9. Unit 1 Foundations of Geometry Angles
If mFPB=70° and mFPS=110° find all angle measures. F H P R S B

10. Unit 1 Foundations of Geometry Angles
Special Angle Pairs
Adjacent Pair:
Linear Pair…
Supplementary:
Complimentary…
Vertical angles…
Common vertex, share side, no common interior points, coplanar
Adjacent angles that form straight line
Two angles whose sum = 180°
Two angles whose sum = 90°
Two nonadjacent angles formed by intersecting lines.

11. Unit 1 Foundations of Geometry Angles
Name all adjacent angle pairs 1 4 2 3 5
Name all linear angle pairs
Name all vertical angle pairs
What angle is complementary to 2x -28°?
What angle is supplementary to 3x + 88°?

12. Homework 1.3(24):12-14,17,18,29,31,33,41,43,44,47 1.4(32):15-17,19,20,27,31,33,44,46