Download Geometry Geometric Figures

Geometry
Geometric Figures
Square
2
Area = s
Perimeter = 4 s
Rectangle
Area = l w
Perimeter = 2 l + 2 w
Parallelogram
Area = b h
Triangle
Area =
1
b h
2
Sides of a Right triangle
Pythagorean formula: a
2
b2
c2
Trapezoid
Area =
1
( a b) h
2
Circle
Area =
r2
C 2 r
2r
Circumference,
Diameter,
d
Sphere
Surface area = 4 r
2
4 3
r
Volume = 3
Cube
Surface area = 6s
Volume = s
2
3
Rectangular solid
Surface area =
Volume =
2lw 2lh 2wh
lwh
Right circular cylinder
Surface area = 2 rh
Volume =
2 r2
r 2h
Circular cone
Surface area =
rs
r2
1 2
r h
Volume = 3
s = Slant Height
LSC-Montgomery Learning Center: Geometry
Last Updated April 13, 2011
Page 2
Common Symbols
is equal to
is perpendicular to
is not equal to
is parallel to
~
is approximately equal to
3.14 or 22/7
Angle
Measure of angle
m
Triangle
a
b
right angle
or
is similar to
is congruent to
is not congruent to
line segment joining points A and B
a:b
ratio of a to b
Common Geometric Terms & Definitions
Right angle
An angle whose measure is 90
Straight angle
An angle whose measure is 180
Acute angle
An angle whose measure is greater than 0 and less than 90
Obtuse angle
An angle whose measure is greater than 90 and less than 180
Complementary angles
Two angles whose sum is 90
Supplementary angles
Two angles whose sum is 180
Polygon
A geometric figure with 3 or more sides
Triangle
A polygon with 3 sides and 3 angles
Equilateral triangle
All sides are equal
Equilateral triangle
All angles are equal (each angle equals 60 )
Isosceles triangle
Two sides are equal (or two angles are equal)
Scalene triangle
All sides are of different lengths
Right triangle
One angle is a right angle
Obtuse triangle
One angle is an obtuse angle
Acute triangle
All three angles are acute
sum of
In any triangle, the sum of the measures of the angles is 180
m( A) + m( B) + m( C) = 180
Trapezoid
A four-sided figure with one pair of parallel sides
Parallelogram
A four-sided figure with two pairs of parallel sides
LSC-Montgomery Learning Center: Geometry
Last Updated April 13, 2011
Page 3
Angles derived from intersecting lines
A transversal is a line that intersects two or
more coplanar lines in different points.
1 2
4 3
When a transversal intersects a pair of lines,
eight (8) angles are formed. Certain pairs of
these angles have special names.
5 6
8 7
Vertical (Opposite) Angles
1 and 3
2 and 4
5 and 7
6 and 8
Corresponding Angles
1 and 5
2 and 6
3 and 7
4 and 8
THE VERTICAL ANGLE PROPERTY:
Vertical angles are congruent
1= 3
2= 4
5= 7
6= 8
Interior Angles
4 and 5
3 and 6
Alternate Interior Angles
3 and 5
4 and 6
Properties of Parallel Lines
If a transversal intersects two parallel lines
A
C
( AB // CD ), then
1 2
4
B
3
5 6
8 7
D
The alternate interior angles are
congruent
3= 5
4= 6
LSC-Montgomery Learning Center: Geometry
Last Updated April 13, 2011
The corresponding angles are
congruent
1= 5
2= 6
3= 7
4= 8
The interior angles on the same side of
the transversal are supplementary
4 + 5 = 180
3 + 6 = 180
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