The document defines and provides examples of parallel lines, perpendicular lines, vertical angles, supplementary angles, corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It also includes illustrations and notations for each type of angle or line. Examples are worked through to find the measures of missing angles based on properties of these angles and lines.
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5. ∗ Def: Lines that intersect to form a right angle.
∗ Illustration:
∗ Notation: m ⊥ n
∗ Key Fact: 4 right angles are formed.
PERPENDICULAR LINES
m
n
5
7. ∗ Def: a line that intersects two lines at different points
∗ Illustration:
Transversal
t
7
8. ∗ Two angles that are opposite angles.
Vertical Angles
1 2
3 4
5 6
7 8
t
∠1 ≅ ∠ 4
∠2 ≅ ∠ 3
∠5 ≅ ∠ 8
∠6 ≅ ∠ 7
9. ∗ Find the measures of the missing angles
Vertical Angles
125 °
?
?
55 °
t
55 °
125 °
10. ∗ Two angles that form a line (sum=180°)
Supplementary Angles/
Linear Pair
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
11. ∗ Find the measures of the missing angles
Supplementary Angles/
Linear Pair
? 72 °
?
t
108 °
108 °
180 - 72
12. ∗ Two angles that occupy corresponding positions.
Corresponding Angles
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
12
13. ∗ Find the measures of the missing angles
Corresponding Angles
145 °
?
t
35 °
145 °
14. ∗ Two angles that lie between parallel lines on opposite sides
of the transversal
Alternate Interior Angles
t
∠3 ≅ ∠ 6
∠4 ≅ ∠ 5
1 2
3 4
5 6
7 8
14
15. ∗ Find the measures of the missing angles
Alternate Interior Angles
82 °
?
t
98 ° 82 °
16. ∗ Two angles that lie outside parallel lines on opposite sides of
the transversal
Alternate Exterior Angles
t
∠2 ≅ ∠ 7
∠1 ≅ ∠ 8
1 2
3 4
5 6
7 8
16
17. ∗ Find the measures of the missing angles
Alternate Exterior Angles
120 °
?
t
60 ° 120 °
18. ∗ Two angles that lie between parallel lines on the same sides
of the transversal
Consecutive Interior Angles
t
∠3 +∠5 = 180
∠4 +∠6 = 180
1 2
3 4
5 6
7 8
p. 131 & 143
30
19. ∗ Find the measures of the missing angles
Consecutive Interior Angles
?
t
135 °
45 °
180 - 135
