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Important Theories Involving Angles
1. Complimentary Angles
- a pair of angles whose sum is 90 degrees
a + b = 90
a
b
2. Supplementary Angles
- a pair of angles whose sum is 180 degrees
a + b = 180
3. Angle Sum of a Triangle (AST)
- the sum of the 3 angles in a
triangle is 180 degrees
a + b + c + 180
b
b
c
a
b
a
d
a
c
e
4. Vertically Opposite Angles
- when 2 lines cut each other, the opposite
angles are equal
c=d
a=b
c
a
b
d
Oct 5­2:02 PM
Theories Involving Tranversals
A tranversal is a line that intersects 2 parallel lines. This forms 8 angles.
1
3
6
5
7
2
4
8
6. Interior Angles
- interior angles on the same side of the transveral are
supplementary
- C rule
- 4 + 6 = 180 degrees
- 3 + 5 = 180 degrees
7. Corresponding Angles
- are equal
- F rule
-1=5
-2=6
-3=7
-4=8
8. Alternate Interior Angles
- are equal
- Z rule
-3=6
-5=4
Oct 5­2:10 PM
9. Isoceles Triangles
-angles opposite to equal sides are equal
a
10. Angle Sum of a Quadrilateral
- the sum of the angles is 360.
b
a
Oct 7­6:05 PM
Elementary School Review
Obtuse
Acute
Right
11. Scalene Triangle
12. Equilateral Triangle
13. Right Triangle
14. Square
- 4 congruent sides, 4 right angles
15. Rectangle
- opposite sides equal, 4 right angles
16. Parallellogram
- 2 pairs of parallel and congruent sides
17. Rhombus
- 4 congruent sides, 2 obtuse angles,
2 acute angles
18. Trapezoid
- 4 sided figure with 1 set of parallel sides
Oct 5­2:16 PM
a
c
d
Find the missing angles
and state reasons why
d­ 59 (supplementary angles)
e ­ 69 (angle sum of a triangle ­ AST)
i ­ 128 (supplementary)
j ­ 52 (vertically opposite)
k ­ 128 (vertically opposite or supp)
g ­ 48 (AST)
h ­ 132 (supplementary)
Oct 7­6:23 PM
Determine the value of x and y.
xo
yo
150o
3xo
2xo
4xo
Oct 2­9:09 AM
Oct 3­2:46 PM
Oct 3­9:16 AM
Oct 3­2:44 PM
Oct 3­9:15 AM
Oct 3­9:15 AM
Oct 11­4:56 PM
Oct 6­2:46 PM
Oct 6­2:43 PM
Oct 6­11:31 AM
Homework Quiz
For the following, determine the value of x and justify your answer!
Oct 5­6:14 PM
Homework Quiz (October 7, 2008)
For the following, determine the value of x and justify your answer!
x
100o
x
60o
x
x
40o
50o
60o
x
80o
100o
x
Oct 5­6:14 PM
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