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BASIC GEOMETRIC FORMULAS AND PROPERTIES
This handout is intended as a review of basic geometric formulas and properties. For further or more advanced geometric formulas and properties, consult with a SLAC counselor.
r
Square:
Perimeter: P = 4s or 2s + 2s
Area: A = s^2
s
s
Rectangle: l
w
Perimeter: P = 2w + 2 l
Area: A = l × w
Triangles:
Perimeter: P = a + b + c
a (^) h c b
Area: A = (1/2) × b × h
Types of Triangles:
Isosceles (two equal sides) Equilateral (all sides equal) Right (one 90o (^) or right angle) A c b B (^) a C
Pythagorean Theorem (for right triangles only):
a^2 + b 2 = c^2
Sum of the Angles (all triangles):o
A + B + C = 180
iameter:
Circle:
D d = 2r
Circumference: C = 2 π r = π d
Area: A = π r^2
Rectangular Solid: l
w h
Volume: V = l × w h
w) + (
×
Surface Area: S = (2 × h× × l × h ) + (2 × l × w)
R ight C ircular Cylinder:
Volume: V = π r h^2
r h
Surface Area: S = 2 π r h + 2 π r^2
mentaryures les A les.
C omplementary Angles:
Two angles are compleif the sum of their meas A C B D
is 90 complementary angles. Ango. Angles A and B are and C are complementary ang
upple
pplementary angles. Angles^ d 2 are ntary angles.
Oppos o lines,
s).
Angles 2 and 3 are congruent. Angles:
re also alternate interior angles. re called alternate
ior nt.
re also alternative exterior angles. nt. (opposite/vertical angles) Angles 4 and 5 are congruent. (alternate interior angles)
Straight lines have degrees measuring B is a straight line,
m 3
S mentary Angles: Two angles are supplementary if the sum of their measures is 180o^. Angles 1 an su 2 and 4 are suppleme m 1 2 1 4 3
m 2 6 5 8 7
ite/Vertical Angles: he intersection of tw m and m , form four
T 1 3 angles. Opposite (vertical) angles are congruent (have equal measure Angles 1 and 4 are congruent.
Alternate Interior and Exterior Lines m 1 and m 2 are parallel. Angles 4 and 5 are called alternate interior angles. Alternate interior angles are congruent. Angles 3 and 6 a Angles 2 and 7 a exterior angles.
Alternate exter angles are congrue Angles 1 and 8 a Note: Angles 1 and 4 are congrue Angles 5 and 8 are congruent. (opposite/vertical angles) Angles 1 and 8 are congruent. (alternate exterior angles) Angles 2 and 6 are congruent. (corresponding angles) Angles 3 and 7 are congruent. (corresponding angles) etc.
Straight Lines: (^180) then angle DCB is 180o. If D to (^) o. D^ C^ B
SOLUTIONS/ANSWERS
- P = a + b + c27 = 7 + 13 + c 7 = c (c = 7 centimeters)
- (^) A = (1/2)A = (1/2) A = 16 (A = 16)units^2
- (^) A = 49A = s^2 A = 7s = 7 2 (s = 7 ft.)
P = 28 (P = 28 ft.)
( l = 9 units)
- (^) tells us another angle is 70g h one 90o^ angle o Angles: A + B + C = 180 90 o (^) + 70o (^) + C = 180o o C = 20o^ (C = 20o)
- c 2 52 2 = (b = 3 units)
- 16
× × b 8 (^) ×× h 4
P = 4(7) A = l × w 36 = l × 4 9 = l Problem^ Right tr^ ian le^ as Sum of
Right Triangles a (^2) + b = 4 + b^2 22 = 16 + b b 2 = 9= 25 b 3 A = π r^2 π (^) = π r^2 π
π π
(^16) = r^2 16 = r^2 (d = 8 units)
d = 2r = 2(4) = 8^ r = 4 C = 2 π 4 C = 2 C = 8 π π (4) ( π =3.14) 25.13 (C = 25.13 units)
V = 240 = 125 = w w (^4) (w = 5 in.)
C = 8(3.14) C = l × w × h × × V = V = π π × r^2 × h V = π ××^242 ×^ × 7 7 V = 28(3.14)V = 87 92. ( π= 3.14) (V = 87.92 unit (^3) )
- h 60 gree measure of 180o (Angle 1 = 60o (^) ) Angle 1 0 o^ (above)(alternate exterior of angle 1) ( osite/vertical of angle 8) (Angle 5 = 60o^ )
- posite in rior of angle 5 ab
o m)^2 ] OR
repared by: Jefferson Humphries, 1989. Revised by: Ziad Diab, 1994 TUDENT LEARNING ASSISTANCE CENTER (SLAC) evised: Summer 2005 exas State University-San Marcos
Straig t lines have a de 180 o (^) - 120o (^) = o
- (^) Angle 8 = 60= 6o Angle 5 = 60o^ opp Angle 4 = 60o^ (op te ove) OR (straihave a degree measure of 180 ght lin s [the diagonal ofe
(opposite vertical with angle 1) (Angle 4 = 60o^ )
P R S T
