1. Chapter 1 Test Tuesday, August 29th
Chapter 1 Student Notes
Chapter 1 Test
Tuesday, August 29th

2. 1.1 Points, Lines and Planes

3. Point - A B

4. Line - C D m

5. Collinear - T / F A and B are Collinear T / F A and C are Collinear
A B C
T / F A and B are Collinear
T / F A and C are Collinear
T / F A, B and C are Collinear

6. Plane - A
B C P

7. Coplanar - Name 3 Coplanar Points ________
Name 3 Noncoplanar Points _________
T/F C, D and G are coplanar
T/F A, B, E, F are coplanar
T/F A, B, C, E are coplanar
A B
C D G
E F

8. Draw and Label each of the following
n and m intersect at P
p contains N
P contains A and B, but not C

9. Draw and Label each of the following
4. m intersects P at X
5. P and R intersect at m

10. 1.2 Segments Objective: Learn the language of Geometry
Become familiar with segments and segment measure

11. Line Segment - A B

12. Betweenness of Points -A B C

13. Measure of a Segment - M 6 N

14. Segment Congruence - R 7 T S 7 U

15. Segment Congruence is marked on a figure in the following manner.12 12 B C

16. Multiple Pairs of Congruent SegmentsD
From the markings on the above figure, make 2 congruence statement. B C

17. A is between C and D. Find Each Measure.
AC = 4, AD = 3, Find CD = ______
CD = 15, AD = 7, Find AC = _____
C A D
C A D 15

18. A is between C and D. Find Each Measure.
3. AC = x + 1, AD = x + 3, CD = 3x – 5, Find x = _____
C x A x D
3x - 5

19. A is between C and D. Find Each Measure.
AC = 8, AD = 5, Find CD = ______
CD = 20, AD = 12, Find AC = _____
C A D
C A D 20

20. A is between C and D. Find Each Measure.
3. AC = 2x + 1, AD = 2x + 3, CD = 5x – 10, Find x = ___
C 2x A x D
5x – 10

21. C is between A and B in each figure. Select the figure that has AB = 12. Select all that apply.
A. C is between A and B.
B. B is between A and D.
A C B
D B A
B is between A and D.
AB = 2x + 5, BD = 3x + 4, AD = 6x – 3
B is between A and D.
AB = 2x + 2, DB = 4x +2, DA =34
D B A
D B A
Answer: ____________

22. 1.3 Distance and Midpoint

23. Distance on a Number Line =
Use the number line to find the length of each segment.
A B C D
AB =
BC =
AD =
BD =

24. Distance on a Coordinate Plane
Formula
Find the length of each segment.
AB =
A(2, 2)
B(-4, 1)
C(2, -4)

25. Find the length of each segment.BC
A(2, 2)
B(-4, 1)
C(2, -4)

26. Midpoint on a Number Line
A B C D
Find the midpoint of each segment.
1. AB
2. AD

27. Find the midpoint of each segment.
A B C D
3. BC
If A is the midpoint of EC, what is the location
for point E?

28. Midpoint on a Coordinate Plane
x1 + x2 , y1 + y2
A(2, 2)
Find the midpoint of each segment.
1. AB
B(-4, 1)
= ( )
= ( )
C(2, -4)

29. Midpoint on a Coordinate Plane
Find the midpoint of each segment.
1. BC
= ( )
A(2, 2)
= ( )
B(-4, 1)
C(2, -4)

30. Midpoint on a Coordinate Plane
Find the midpoint of each segment.
2. AC
= ( )
A(2, 2)
= ( )
B(-4, 1)
C(2, -4)

31. M is the midpoint of AB. Given the following information, find the missing coordinates.
x1 + x2 , y1 + y2
M(2, 6) , B(12, 10) , A ( ? , ? )

32. M is the midpoint of AB. Given the following information, find the missing coordinates.
x1 + x2 , y1 + y2
M(6, -8) , A(2, 0) , B ( ? , ? )

33. 1.4 Angle Measure

34. Ray - R B A D S E

35. Angle–

36. Points _______________________________ G ____________________
Angles and Points
Points _______________________________
G ____________________
H ____________________
E ____________________ D G H F E

37. ________ Naming Angles D G H F 2 E
Name the angle at the right as many ways as possible.
________ D G H F 2 E

38. Naming Angles _______ _______ J M L 3 2 K
Name the angles at the right as many ways as possible.
_______
_______ J M L 3 2 K

39. Naming Angles _________ J M L 3 2 K
Name the angles at the right as many ways as possible.
_________ J M L 3 2
There is more than one angle at vertex K, K ●
__________________ ____________________________________ ●

40. ________ different types of angles:
Right angle:
Acute angle:

41. Can also be called __________ ________________.
Types of Angles
Obtuse angle:
Straight angle:
Can also be called __________ ________________.

42. Congruent Angles
33o W M
33o

43. Multiple Sets of Congruent AnglesB
__________ C D

44. Angle Bisector _________________ or ________________
KM is an angle bisector.
What conclusion can you draw about the figure at the right? J M
_________________ or
________________ 4 L 6 K

45. _____________________________.
Adding Angles
4/21/2017
When you want to add angles, use ______________________ _____________________________________________________________..
If you add m1 + m2, what is your result?
_____________________________. J M
48o
28o L 1 2 ● K

46. Angle Addition Postulate
The sum of the two smaller angles adjacent angles will _______________________________________________________________________________________________. R U 1 T 2
Complete:
m ______ + m  ______ = m  _______ or S

47. Example Draw your own diagram and answer this question:
If ML is an angle bisector of PMY and
mPML = 87, then find:
mPMY = _______
mLMY = _______

48. JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4
JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4. Find x and mLJM. L
(4x + 10)o K
(6x – 4)o J M
mLJM = _____

49. RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3
RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x Find x and mPRS. P S
(4x + 3)o R T
mPRS = ___

50. 1-5 Angle Pairs

51. Complementary Angles -
Examples: M R D 1 2 N S T
Perpendicular – _______________________

52. Supplementary Angles-
Examples: G L 2 1 H J K K

53. Adjacent Angles

54. Adjacent Angles 3 4

55. Vertical Angles-
Example: C A 3 2 1 E 4 B D

56. Theorem: C ● A 3 2 1 E 4 D B

57. What’s “Important” in Geometry?
4 things to always look for !
Most of the rules (theorems)
and vocabulary of Geometry
are based on these 4 things.
. . . and ___________( )

58. Examples 1 & 2 are complementary. m1 = 4x + 5,
m2 = 5x Find x and the measure of each angle.
x = _____
m1 = _____
m2 = _____

59. Examples 5 & 6 are supplementary. m5 = 10x + 12,
m6 = 2x Find x and the measure of each angle.
x = _____
m5 = _____
m6 = _____

60. Examples 2 4
m1 = 2x + 7, m3 = 3x – 3. Find x and the measure of each angle.
Find x = _____
m 2 = _____
m1 = _____

61. Examples 2 4
m2 = 5x + 12, m4 = 7x – 20.
Find x and the measure of each angle.
x = _____
m 2 = _____
m1 = _____

62. 1.6 Polygons

63. Determine if each figure is a polgyon
Polygon -
Determine if each figure is a polgyon

64. Concave Polgons
Example of Concave Polygons

65. Convex Polygons
Examples of Convex Polygons

66. Number of Sides 3 4 5 6 7 8 9 10 11 12 13 n
Name of Polygon
Hint

67. Regular Polygon-
Examples of Regular Polygons

68. distance around a polygon
Perimeter -
distance around a polygon
Find the perimeter of each polygon.
Regular Hexagon
Rectangle
Square
3cm
4ft
8in
6cm
P = _______
P = ________
P = ______

69. Name each polygon by its number of sides
Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.

70. Name each polygon by its number of sides
Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.

71. Find the perimeter and area of the polygon below.
8cm
P = ________
3cm
5cm
5cm
5cm
A = ________
5cm
3cm
8cm

72. Triangle ABC has the following coordinates. Find the perimeter of ABC.