Math 7 - Q1 W1 Introduction to Geometry (SY 2024-2025).pdf

Math 7 Introduction to Geometry is all about the fundamental concepts needed to fully understand the succeedding lessons in Geometry.

1. Undefined Terms
in Geometry

2. Point
…It has no dimensions (length, width, height).
…It is usually represented by a capital
letter and a dot on a page.
BA
Examples:
C
D E
…It only designates location.
They are named as:
Point A
Point B
Point C
Point D
Point E

3. Line
…It has only one dimension (has length
but no width or "thickness“)
…Its length extends in one dimension
and goes on forever in both directions.
B
A
Example:
m
It is named as:
Line AB
Line m
ABor

4. Plane
…It is a flat surface.
…It has no thickness but extends
indefinitely in all directions.
BA
Example:
m It is named as:
Plane ABC
Plane m
C

5. Space
…It is the set of all possible points; made
up of infinite planes
…It has three dimensions; sometimes we
say length, width and height.

6. Subsets
of a Line

7. Ray
…has one endpoint and extends only in one
direction.
Examples:
C
Ray CD
Subsets of a Line:
D
CDor
E
F
Ray EF EFor

8. Line Segment
…It has two end points.
Examples:
G
Line Segment GH or HG
Subsets of a Line:
H
or
J
K
GH HG
Line Segment JK or KJ
orJK KJ

9. E
C
H
G
D
A
B
K
Group A Group B
A, B & D
A, E & B
A, E & D
D, B & E
C, B & K
B, A & H
C, G & A
H, D & G
H, E & D

10. Collinear Points
…are points lying on the same line.
Non-Collinear
Points
…are points that do not lie on the same
line.

11. E
C
H
G
D
A
B
K
Group A Group B
A and E
A and BA and H
H and EB and E
C and AC and D
B and GH and K
G and K
B and H
C and K

12. Coplanar Points
…are points lying on the same plane.
Non-Collinear Points
…are points that do not lie on the
same plane.

16. -Three or more lines that have a common point.
a
b X
d
e
M
g
h
P
c
f
i

18. -coplanar lines that intersect at one point.
a
b
X
c
d
M
e
f
P

20. -coplanar lines that do not intersect.
g
h
i
j
k
l

22. -are noncoplanarlines and do not intersect.
m
q
t
n
O
p
R
s
U

25. Definition of Congruent Segments
��is congruent to ��  
A B C D
The length of ��is equal to the length of ��
��≅��
��=��

26. Definition of Congruent Segments
��is congruent to ��  
A B C D
The length of ��is equal to the length of ��
��≅��
��=��

27. Definition of Midpoint  
Bis the midpoint of ��
A CB
��is congruent to ��
��≅��

28. Definition of Perpendicular Lines  
��is perpendicular to��
J K
∠�??????�, ∠�??????�, ∠�??????�, &
∠�??????�are right angles
��⊥��
L
M
O

29. Let’s learn about

30. How well do you
understand
angles?

31. 1. What is the VERTEXof
∠���?
Answer: S
T
O
H
S

32. 2. Which of the following is the
SIDEof ∠OST?
A.��
B.�??????
C.??????�
D.��
T
O
H
S

33. 3. Which of the following is an
angle whose VERTEXis S?
A.∠SHO
B.∠TSO
C.∠TOS
D.∠THS

34. 4. Which of the following is an
angle whose VERTEXis O?
A.∠SHO
B.∠TSO
C.∠TOS
D.∠THS

35. 5. Which of the following points
is in the INTERIORof ∠YES?
Y
.O
S
E
.X
.N
A
A.Y
B.N
C.O
D.E

36. 6. Which of the following points is
at the EXTERIORof ∠YEA?
Y
.O
S
E
.X
.N
A
A.O
B.X
C.A
D.E

37. 7. Which of the following is
TRUEabout the given figure?
A.∠2 is another name for ∠PXR
B.R is in the interior of ∠QXP
C.∠1 is the same as ∠PXQ
D.There are 3 distinct angles
with vertex X
Q
R
X
P
2
1

38. 8. Which of the following is
a RIGHT ANGLE?
A.∠VOE
B.∠LOV
C.∠EOL
D.∠EOV
L
V
E
O

39. 9. Which of the following is
an OBTUSE ANGLE?
A.∠VOE
B.∠LOV
C.∠EOL
D.∠EOV
L
V
E
O

40. 10. Which of the following
is an ACUTE ANGLE?
A.∠VOE
B.∠LOV
C.∠EOL
D.∠EOV
L
V
E
O

41. 11. How many ANGLESare
there in the figure?
Answer: 14

42. 12. Which of the following is the
MEASUREMENT of an ANGLE?
A.from 0
o
to 90
o
B.between 0
o
and 90
o
C.from 0
o
to 180
o
D.between 0
o
and 180
o

43. A.
B.
C.
13. Which of the following
shows a 75
O
ANGLE ?

44. A. B.
C.
14. Which of the following
shows a 150
O
ANGLE ?

45. 15. Which equation shows the correct
ANGLE ADDITION POSTULATE ?
A.∠1 + ∠2 =∠LOV
B.m∠1 + m∠2 =m∠LOV
C.∠1 + ∠2 =∠EOV
D.m∠1 + m∠2 =m∠EOV
L
V
E
O
2
1

46. Let’s see who
performed well…
15: Excellent!
11-14: Very Good!
5-10: Good!
1-4: OMG!
0: Stressful!

47. Let’s learnMORE about

48. CONGRUENT ANGLES
2
1
-angles with equal
measurements
4
3
∠�≅∠�
∠�≅∠�

49. ADJACENT ANGLES
5
6
A
B
-Two angles that share the same vertex and
have one side in common between them.
∠�and ∠�
are adjacent
angles
78
C
D
∠�and ∠�
are adjacent
angles

50. COMPLEMENTARY ANGLES
10
9
62°
-the sum of two angle measures is 90 degrees.
??????∠�+??????∠��=��
H
O
N
??????∠���+??????∠??????��=��
28°
If ??????∠���=��
What is ??????∠??????��?
S
E
T

51. SUPPLEMENTARY ANGLES
1112
58°
-the sum of two angle measures is 180
o
.
??????∠��+??????∠��=���
S
I
M
??????∠���+??????∠��??????=���
122°
If ??????∠��??????=��
What is ??????∠���?
L
P
E

52. LINEAR PAIR
12
60°
-Two angles that are adjacent and
supplementary.
∠�and ∠�form a linear pair
??????∠�+??????∠�=���
120°

53. 34
56
55°
VERTICAL ANGLES
-angles opposite each other when two lines
intersect are vertical angles.
-Vertical angles are always congruent.
∠�and ∠�
are vertical angles
∠�≅∠�
125° ∠�and ∠�
are vertical angles
∠�≅∠�
55°
125°

54. ANGLE BISECTOR
G
E
O
M
45°
-Divides an angle into two congruent parts.
??????�bisects ∠�??????�
∠�??????�≅∠�??????�
45°
If ∠�??????�is a right
angle, what is
??????∠�??????�and
??????∠�??????�?

55. Let’s sum up
everything
about angle
relationships…

56. What angles are
complementary and
supplementary to 37
o
?
Answers:
53
o
and 143
o

57. What is the measure of each of
the congruent angles, if a 170-
degree angle is bisected?
Answer: 85
o

58. What is the value of the
larger complementary angle,
if ??????∠1 = 2x and ??????∠2 = 3x?
Answer: 54
o

59. What are the two
perpendicular
lines in the
figure?
Answer: ��⊥��

60. What is
??????∠�?????????????
Answer: ��

61. What’s your score?
5: Excellent!
4: Very Good!
3: Good!
2: OMG!
1: Stressful!
0: SSAD!