[PDF] BASIC GEOMETRIC FORMULAS AND PROPERTIES

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BASIC GEOMETRIC FORMULAS AND PROPERTIES

ndout is intended as a review of basic geometric formulas and properties For further or more 

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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 + 2l

Area: A = l w

Triangles:

Perimeter: P = a + b + c

a c h b

Area: A = (1/2) b h

Types of Triangles:

Isosceles (two equal sides)

Equilateral (all sides equ

al)

Right (one 90

o or right angle) A c b B C a

Pythagorean Theorem (for right triangles only):

a 2 + b 2 = c 2

Sum of the Angles (all triangles):

o

A + B + C = 180

iam eter:

Circle:

Dd = 2r

Circumference: C = 2 r = d

Area: A = r

2

Rectangular Solid:

l w h

Volume: V = l w

h w) + (2

Surface Area: S = (2 h l h ) + (2 l w)

ight C

Rircular Cylinder:

Volume: V = r

h 2 r h

Surface Area: S = 2 r h + 2 r

2 mentary ures les A les. omplementary Angles: C Two a ngles are comple if the sum of their meas C A D B is 90 o . Angles A and B are complementary angles. Ang and C are complementary ang upple d 2 are pplementary angles. Angles 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 180 o

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 13 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
o . If D to D C B then angle DCB is 180 o 2 4 8 5 4 b

BASIC PROBLEMS OF GEOMETRY

1. Two sides of a triangle are 7 andind the third side.

. If a square has an area of 49 ft 2 , what is the length of one of its sides? The perimeter? how long must its length be . of a right triangle is 70 o , what are the other 2 angles? . What is the diameter of a circle with an area of 16

13 centimeters. The perimeter is 27 centimeters. F

2. Find the area of the triangle:

3

4. If a rectangle has a width of 4,so that the area is 36?

If one angle5

. Find b: 6 7? . What is the circumference of the circle in problem 7? (allow

8 = 3.14)

d a ume 240 in. 3 , what is the box's . If a box has a height of 4 in., a length of 12 in., anvol9 width?

10.Find the volume: (allow = 3.14)

11. Lines m

1 and m 2 are pa

2. What is the measure of angle 5?

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