1. GEOMETRY
Chapter 1

2. CONTENTS Naming Figures Describing Figures Distance on a number line
Distance on a grid
Segment Addition Postulate
Angles and Their Measures
Measuring Angles
Angle Addition Postulate
Classify Angles
Segment Bisectors and Midpoints
Angle Bisectors

3. NAMING FIGURES l FIGURE DESCRIPTION NAME IT A POINT A B D C 3 POINTS
B, C, D
A line containing 3 known points E F G l FE FG EF GE OR
.....
OR l H J
A segment with 2 end points HJ JH OR

4. NAMING FIGURES FIGURE DESCRIPTION NAME IT OR KL KM R, S, & T
Ray with endpoint K OR KL KM M L K
Collinear points
R, S, & T R T S U
Noncollinear points
U, R, S, & T
Opposite rays are two rays that share the same endpoint and they form a line. X Z Y
and YX YZ

5. NAMING FIGURES NAME IT FIGURE DESCRIPTION Q NOP OR Q
A plane containing 3 known points OR

6. DESCRIBING FIGURES Describe the figure: yO P Q R
Plane Q contains Line NP, Line PR,
and Points N, P, R, and O.
Line NP and Line PR intersect at
Point P.
Line y intersects plane Q at point O.

7. DISTANCE On a Number Line = 13 Finding the length of a segment is
the same as finding the distance
between its endpoints. When we
measure a segment and attach a
number to it we drop the bar in the
symbol:
Since the length of AB is 12, we
write AB = 12. E F G
-15 -2 7
The length of FG is | F – G |.
FG = | F – G |
= | -15 – - 2 |
= | |
YOU TRY: Find GE and FE.
= | -13|
= 13

8. DISTANCE On a Number Line Find GE and FE.
-15 -2 7
The length of GE is | G – E |.
GE = | G – E |
= | - 2 – 7 |
= | - 9|
= 9
The length of FE is | F – E |.
FE = | F – E |
= | - 15 – 7 |
= | - 22|
= 22

9. DISTANCE On a Number Line Find the length of the segment that has
endpoints with coordinates P(16) and Q(- 4).
The length of PQ is | P – Q |.
PQ = | P – Q |
= | 16 – - 4 |
= | 20|
= 20

10. DISTANCE On a Grid To find the distance between two points on a
Grid, use the Distance Formula:
Subtract x-values
Subtract y-values
Square the result
Square the result
Add the results
Take the SQUARE ROOT and simplify

11. Example: Find the distance between
On a Grid
Example: Find the distance between
A( - 10, 4) and B( - 6, 1)
AB = 5

12. DISTANCE
On a Grid
Find the distance between C( 7, - 3) and D( - 5, 2)
CD = 13

13. Segment Addition Postulate
If B is between A and C, A C B
Then AB
+ BC
= AC

14. Segment Addition Postulate
If W is between X and Z,
XW = 24 ,
WZ = 53 ,
Find XZ . X Z W 53 24 XW
+ WZ
= XZ 24
+ 53
= XZ 77
= XZ

15. Segment Addition Postulate
If W is between X and Z,
XW = 69 ,
XZ = 142,
Find WZ .
142 X Z W 69 XW
+ WZ
= XZ 69
+ WZ
= 142
– 69
– 69
WZ = 73

16. Segment Addition Postulate
If G is between P and M,
PG = 4x + 6 ,
MP = 9x + 12,
and MG = 3x + 26,
Find all three segment measures .
9x + 12
4x + 6 P G
3x + 26 M PG
+ MG
= MP
4x + 6 +
3x + 26
9x + 12 =

17. Segment Addition Postulate
4x + 6
3x + 26 = =
9x + 12
9x + 12 + 7x
+ 32 =
9x + 12
- 7x
- 7x 32 =
2x + 12
- 12
- 12 20 = 2x 10 = x
PG = 46
MG = 56
MP = 102
PG = 4x + 6 = 4(10) + 6 = 46
MG = 3x + 26 = 3(10) +26 = 56
MP = 9x + 12 = 9(10) + 12 = 102

18. Angles and Their Measures J
Angle symbol 1
sides K L
Naming angles (4 ways)
1) JKL
2) LKJ
3) K (only if 1 angle)
4) 1 K
KJ and KL form JKL K
Vertex is K

19. Naming Angles
ONP or
PNO
MNP or
PNM
MNO or ONM

20. Interior of an Angle

21. Adjacent Angles  Common vertex Common ray No interior points in

22. Congruent angles are angles Angle Measures are equal!!
Measuring Angles 
Congruent angles are angles
with the same measure.
If m ABC = 50 and m JKL = 50
Then ABC  JKL
Angles are congruent
Angle Measures are equal!!

23. Angle Addition Postulate
If P is in the interior of  RST,
then m RSP + m PST = m RST . R P S T

24. Angle Addition Postulate
Suppose that the angle at the right measures 60° and that there is a point K in the interior of the angle such that m GHK = 25 .
Find m KHI .
25°
60° K ?°
m GHK + m KHI = m GHI
x =
m KHI = 35
X = 60 – 25 = 35

25. Classify Angles Right Angle 90 Obtuse Angle Acute Angle
90 < x < 180
Acute Angle
0 < x < 90
Straight Angle
180

26. Segment Bisector Bisect means to cut into 2 congruent pieces.
The midpoint of a segment is
the point that bisects the segment.
A segment bisector is a segment, ray, line or plane that intersects the segment at its midpoint.

27. Construct the Midpoint of a Segment

28. If X is the midpoint of AB,
Midpoints
If X is the midpoint of AB, B X A
Then, AX = XB.

29. Midpoints on number lines
To find the midpoint of a segment on a number line, just average the coordinates of the endpoints. 12 47
- 23 24 2 =
= 12 2

30. Endpoints on number lines
To find the endpoint of a segment on a number line with one endpoint and the midpoint: Midpoint x 2, then subtract the known endpoint. 23 60
- 14
23 x = = = 60

31. Midpoint Formula Midpoints on a Grid
The Midpoint Formula:
The midpoint of a segment with endpoints
(x1 , y1) and (x2 , y2)
has coordinates

32. Midpoint on a Grid (- .5, 2.5) A is (-3, 4) B is ( 2, 1) Midpoint is
-3 +2, 4 + 1
( )
(- .5, 2.5)

33. Endpoint on a Grid A segment has endpoint J(-7, 8) and
midpoint P(2, -1). Find the other endpoint.
Double the midpoint P(2, -1).
Then subtract the endpoint you know J(-7, 8).
P(2, -1) x 2 gives (4, -2).
(4, -2) - (-7, 8)
(4 - -7, -2 – 8)
(11, -10)
The other endpoint is (11, -10).

34. Angle Bisectors An angle bisector is a ray that divides
an angle into two adjacent congruent angles.
Angle bisector

35. Construct an Angle Bisector