iam shivraj of 9th d

2. A point is an exact position or location.

3. A series of points that go
endlessly in both directions.

4. Line Segment
A part of a line that has
two endpoints.

5. Ray
Ray is the part of a line that has one
endpoint and goes on endlessly
in the other direction.

6. PaRaLLeL LineS
• Def: line that do not intersect.
• Illustration:
• Notation: l || m AB || CD
l
m
A
B
C
D

7. Examples of Parallel Lines
• Hardwood Floor
• Opposite sides of windows, desks, etc.
• Parking slots in parking lot
• Parallel Parking
• Streets: Laramie & LeClaire

8. Examples of Parallel Lines
• Streets: Belmont & School

9. PERPENDICULAR LINES
• Def: Lines that intersect to form a right
angle.
• Illustration:
• Notation: m ⊥ n
• Key Fact: 4 right angles are formed.
m
n

10. Ex. of PERPENDICULAR
LINES• Window panes
• Streets: Belmont and Cicero

11. Vertex
The point at which two rays
join together to form an
angle.

12. Obtuse Angle
An angle that measures more
than 90 degrees.

13. Acute Angle
An angle that measures
less than 90 degrees.

14. Right Angle
An angle that measures
90 degrees.

15. Straight Angle
An angle that measures
180 degrees.

16. Degrees
The unit used to
measure angles.
7090 11030

17. Adjacent angles
Two angles are said to be adjacent angles if:
1)They have a common vertex.
2)They have a common arm.
3)The non-common arms lie on either side of the common arms.

18. • Def: a line that intersects two lines at
different points
• Illustration:
Transversal
t

19. Vertical Angles
• Two angles that are opposite angles.
1 2
3 4
5 6
7 8
t
∠1 ≅ ∠ 4
∠2 ≅ ∠ 3
∠5 ≅ ∠ 8
∠6 ≅ ∠ 7

20. Supplementary Angles/
Linear Pair
• Two angles that form a line (sum=180°)
1 2
3 4
5 6
7 8
t
∠5+∠6=180
∠6+∠8=180
∠8+∠7=180
∠7+∠5=180
∠1+∠2=180
∠2+∠4=180
∠4+∠3=180
∠3+∠1=180

21. Corresponding Angles
• Two angles that occupy corresponding
positions.
Top Left
t
Top Left
Top Right
Top Right
Bottom Right
Bottom Right
Bottom Left
Bottom Left
∠1 ≅ ∠ 5
∠2 ≅ ∠ 6
∠3 ≅ ∠ 7
∠4 ≅ ∠ 8
1 2
3 4
5 6
7 8

22. Alternate Interior Angles
• Two angles that lie between parallel lines
on opposite sides of the transversal
t
∠3 ≅ ∠ 6
∠4 ≅ ∠ 5
1 2
3 4
5 6
7 8

23. Alternate Exterior Angles
• Two angles that lie outside parallel lines
on opposite sides of the transversal
t
∠2 ≅ ∠ 7
∠1 ≅ ∠ 8
1 2
3 4
5 6
7 8

24. Consecutive Interior Angles
• Two angles that lie between parallel lines
on the same sides of the transversal
t
∠3 +∠5 = 180
∠4 +∠6 = 180
1 2
3 4
5 6
7 8