Algebra ReviewReviewing skills needed to succeed in Geometry.

Solving Proportions• Cross Product Property!!

ad = bc

Solve:

7

6

2

4

x

d

c

b

a

3

20

:

x

Answer

Solve:

• Isolate ratio with variable first by adding 8 to both sides.

• Cross multiply, or think of it as multiplying both sides by 4.

• Answer: k = 80

1284

k

Solve:

• To isolate the variable,multiply both sides by the reciprocal of , which is .

• You get x = . • Reduce your answer by dividing numberator and

denominator by 3. Final answer: x =

3

2

2

3

18

15

6

5

9

5

3

2x

Simplify is different from solve!!• Simplify means leave your expression is in

simplest terms: no like terms remain• May need to distribute or combine like terms• DO NOT SOLVE. If there is no equal sign in the

problem, you don’t solve!!! Don’t add an equal sign if its not there

Simplify: 3(x-4) + 2x

Answer: 5x - 12

FOIL vs. FACTOR

1. Simplify:

(x+6)(x-2)

2. Factor: x2 +4x -12

Linear Equations• Parallel lines = same slope• Perpendicular lines = opposite, reciprocal slope• Vertical lines = undefined slope ( Equation written

as x = a )• Horizontal lines = slope of 0 (Equation written as

y = b)• To find the slope between 2 given points on a line: 12

12

xx

yy

Forms of Equations of a Line• Slope Intercept: y = mx + b

m= slope, b = y intercept

• Standard Form: Ax + By = C

• Point Slope Form: y – y1 = m (x – x1)m = slope, (x1, y1) = any point on the line

Writing Equations of a Line• Need a point on the line and the slope of the line• If given 2 points, find the slope first, then use either point• Use algebra to move back and forth between forms of a line

Example: Write the equation in slope intercept form of the line with a slope of -1 that passes through the point (4, 3).

1. Use the model y = mx +b and substitute 3 in for y, -1 in for m, and 4 in for x.

2. Solve for b. 3. Write equation using the slope(m) and the y-intercept (b)

Answer: y = -1x +7

Examples:

1. Write in slope intercept form the equation of a line with slope 2 passing through (3,-3).

Answer: y = 2x -9

2. Write the equation of the vertical line passing through (6, 2).

Answer: x = 6

The Graph of a Linear Equation• X – intercept : y coordinate= 0• Y- intercept : x coordinate = 0• Can graph using intercepts or in slope-intercept

form• To graph in slope-intercept: graph the y-intercept,

use slope to graph other points• Positive slope: rise to right• Negative slope: fall to the right

Graph the equation: y = -2x + 5

Factoring Special Patterns:

Difference of Two Perfect Squares:(a2-b2) = (a-b)(a+b)

Factor r2 – 25

Answer: (r +5 )(r – 5)

Perimeter, Area, Circumference• Perimeter: The sum of the lengths of the sides of

a polygon (called circumference for circles)• Units of measurement: in, yds, ft, miles, meters, etc..

• Area: The number of square units a polygon encloses• Units of measurement: in2, cm2, mi2, etc…

Rectangle:• base length: b

• height: h

• Perimeter: 2b + 2h

• Area: bh

Example: Find the perimeter and area of a rectangle with base 2 yd and height 5 ft.

Answer: Perimeter = 14 ft; Area = 10 ft2

b

h

Circle:• Radius: r

• Diameter: d =2r

• Circumference: • C= d OR• C= 2 r

• Area: A = r2

d

r

• If directions say leave in terms of , THEN LEAVE THE IN YOUR ANSWER!!!! Otherwise, use button on calculator.

EX. Find the circumference of a circle with a diameter of 4 ft to the nearest tenth.

Find the area of the circle and leave in terms of .

24;6.12: ftAftCAnswers

Triangle:

Area = bh2

1

b

h

SURFACE AREA AND VOLUME

Rectangular Prism:

Surface Area = 2lw + 2 lh + 2 wh

Volume: lwh

Simplifying a Square Root Radical:• No perfect square factor left under the radical• Use the following multiplication property of radicals:Table of perfect squares:

Example: Simplify• Find highest perfect square factor of 50. It is 25 ( 25 X 2 = 50) • Rewrite the radical:• Simplify:

baab

n 1 2 3 4 5 6 7 8 9 10

n2 1 4 9 16 25 36 49 64 81 100

50225225

25

How did we get 5 ??? Square root of 25 is 5.

Triangles, Triangles, and more Triangles• Sum of all angle measures in a triangle is always 180˚• Acute triangle: all angles less than 90˚• Obtuse triangle: one angle more than 90˚• Right triangle: one angle = 90˚

Pythagorean Theorem: used to find missing side lengths in a RIGHT triangle

a2 + b2 = c2

c has to be the hypotenuse (side opposite right angle)

Angles

Made up of 2 rays that intersect at a common point, called the vertex.

Supplementary angles: add up to 180˚Complimentary angles: add up to 90˚

2 lines intersected by a transversal• Line n is the transversal• Creates 8 angles: • Pairs of angles formed are:1. Same side interior ( 4 and 5)2. Alternate interior ( 3 and 5) 3. Corresponding ( 2 and 6) 4. Same side exterior ( 2 and 7) 5. Alternate exterior ( 1 and 7)

When 2 parallel lines are intersected by a transversal:• Corresponding angles are congruent ( meaning of

equal measure)

• Alternate interior angles are congruent• Same side interior angles are supplementary• Alternate exterior angles are congruent• Same side exterior angles are supplementary