[PDF] BASIC GEOMETRIC FORMULAS AND PROPERTIES PDF Basic%20Geometiric%20Formulas%20and%20Properties.pdf

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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):

A + B + C = 180

iam eter:

Circle:

Dd = 2r

Circumference: C = 2 r = d

Area: A = r

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

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

Angles 2 and 7 a

exterior angles.

Alternate exter

angles are congrue

Angles 1 and 8

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:

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?

4 3

m2 6 5

8 7

rallel, what is the measure of angle 1? 1

3. What is the measure of angle 4? 1

m3 m1 120 o 2 7 3

SOLUTIONS/ANSWERS

1. P = a + b + c

27 = 7 + 13 + c

7 = c (c = 7 centimeters)

2. A = (1/2)

A = (1/2)

A = 16 (A = 16)units

3. A = s

A = 49

A = 7 2 s = 7 (s = 7 ft.)

P = 28 (P = 28 ft.)

4. (l = 9 units)

5. g hone 90

o angle tells us another angle is 70 o

Angles: A + B + C = 180

o 90
o + 70 o + C = 180 o

C = 20

o (C = 20 o 6. c 2 5 2 2 = (b = 3 units) 7. 16 bh 84

P = 4(7)

A = lw

36 = l4

9 = l

Right tr

Problem

ianleas

Sum of

Right Triangles

a 2 b = 2 2 2 4+ b=

16 + b

2 = 25 b= 9 b 3 A = 2 r 2 = r 2 16r 2

16 = r

(d = 8 units) 8. r = 4 d = 2r = 2(4) = 8

C = 24

C = 2(4)

C = 8 ( =3.14)

25.13 (C = 25.13 units)

9. V =

240 = 12w4

5 = w (w = 5 in.)

10.

C = 8(3.14)

C = lhw V = r 2 h V = 2 2 7

V = 47

(V = 28(3.14) = 3.14) . (V = 87.92 unit 3 ) V = 8792 4

11. hgree measure of 180

o 60
(Angle 1 = 60 o

Angle 10

o (above) (alternate exterior of angle 1) (osite/vertical of angle 8) (Angle 5 = 60 o

13. posite inrior of angle 5 ab

m 2 o OR repared by: Jefferson Humphries, 1989. Revised by: Ziad Diab, 1994 evised: Summer 2005

TUDENT LEARNING ASSISTANCE CENTER (SLAC)

exas State University-San Marcos

Straigt lines have a de

o 180
o - 120 o

12. = 6

Angle 8 = 60

Angle 5 =60

o opp

Angle 4 = 60

o (opteove) OR (strailins [the diagonal ofght e have a degree measure of 180 (opposite vertical with angle 1) (Angle 4 = 60 o P R S T 5quotesdbs_dbs11.pdfusesText_17

[PDF] [PDF] BASIC GEOMETRIC FORMULAS AND PROPERTIES