GEOMETRY PRETEST REVIEWReviewing skills needed to succeed in

Geometry. Day 1

REDUCING FRACTIONS

5

4

53

43

15

12

Look for common factors, and cancel them out to 1.

SIMPLIFYING EXPRESSIONS What does it mean to simplify?

Look out for the distributive property

Combine like terms

Example:Simplify.

5 STEPS FOR SUCCESSFUL EQUATION SOLVING

Step 1: Perform any distribution; look for ( ).

Step 2: Combine like terms on each side of = sign.

Step 3: Add or subtract variable terms to get all variables on the same side of the = sign.

Step 4: Isolate the variable term by subtracting (-) or adding (+) the constant (number with no variable) from each side of the equation.

Step 5: Isolate the variable by dividing both sides of the equation by the coefficient of the variable term.

Example:Solve.

SOLVING PROPORTIONSoAn equation that shows two equal ratios, such as

oUse the Cross Product Property to solve!!

d

c

b

a

Example:Solve.

ad = bc

THE COORDINATE PLANEHas 4 quadrants

The origin is at (0,0)

Coordinates are . is horizontal coordinate is vertical coordinate

SLOPE

Slope measures how steep a line is.

There are 4 kinds of slope.

To find the slope between 2 points on a line:

12

12

xx

yym

SLOPE Parallel lines have the same slope.

Perpendicular lines have opposite, reciprocal slopes.

Example: Find the slope of the line shown below:

FORMS OF EQUATIONS OF A LINE

We will use this form most often in this course.

WRITING THE EQUATION OF A LINENeed 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 that passes through point (-2, 1) and has a slope of 3.

GRAPHING A LINE USING INTERCEPTS

A x-intercept is where a line crosses the x-axis. To find it algebraically you plug in 0 for y.

A y-intercept is where a line crosses the y-axis. To find it algebraically you plug in 0 for x.

Can graph using intercepts or in slope-intercept form.

GRAPHING A LINE USING To graph in slope-intercept (): Graph the y-interceptUse slope to graph other points

Example:Graph the equation:

y intercept: _____

Slope: ______

#20 in packet: Solve for x and y.

Since y is isolated in equation 1, we can use the substitution

method.

Substitute 3x-5 from the first equation in for y in the second.

Then solve for x.

Use this value to find y.

SOLVING A SYSTEM OF EQUATIONS WITH 2 VARIABLES

FACTORING QUADRATICS

A "quadratic" is a polynomial that looks like ", where "", "", and "" are just numbers.

For the “easy” case of factoring, you will find two numbers that will not only multiply to equal the constant term "", but also add up to equal "", the coefficient on the x-term.

Example: Factor

What two numbers multiply to 12 and add to 8? If you said 6 and 2 you are correct!

Answer:

How do you check your answer?

NICE WORK, MATHLETES!

GEOMETRY PRETEST REVIEW Day 2

Reviewing skills needed to succeed in Geometry.

PERIMETER AND AREA

Perimeter: The sum of the lengths of the sides of a polygon (called circumference for circles)

Units of measurement: in, yd, ft, miles, meters, etc...

Area: The number of square units a polygon encloses

Units of measurement: in2, cm2, mi2, etc…

CIRCLES

Radius: r

Diameter: d =2r

Circumference is the distance around a circle.

Both the circumference and area formula require you to find the radius!

LET’S PRACTICE! Try Problems #1-5 with the person next to you.

I will select some of you to put your answers on the board. Be ready!

AREA OF A TRIANGLE

Area = bh2

1

b

h

PYTHAGOREAN THEOREM

Used to find the missing side length of a right triangle.

MUST be used on a right triangle

c is the hypotenuse, a and b are the legs of the right triangle

a2 + b2 = c2

SIMPLIFYING RADICALS A radical is in simplest form when the number under the radical sign has no perfect square factors other than 1.

Example: 1. Simplify

Try these!2. Simplify

3. Simplify

VOCABULARY

EXAMPLES

BA

or

AB

2. A B A B C

1.

Read “segment AB” or “segment BA”

AC

or

AB

Read “Ray AB” or “Ray AC”. DO NOT write Ray BA or Ray CA. Must name endpoint first!!

VOCABULARY(Please note: In Geometry, it is important to use the correct notations!!)

Notation: Examples:

How you name a line: Use any two points on the line with a line above it, or by a single lower case letter.

How you name a segment: Use the 2 endpoints with a straight line above.

How you name a ray: Endpoint must be first, then any other point on the ray; write an arrow pointing to the right aboveWhat are “opposite rays”?

PLANESA flat surface that has no thickness

Contains many lines

Extends without end in the direction of all its lines

Named by a single capital letter OR by AT LEAST 3 POINTS NOT ON THE SAME LINE

List 2 ways to name the plane shown above. 1. ____________2. ____________

PAIRS OF ANGLESComplementary angles: 2 angles that add up to 90˚

Supplementary angles: 2 angles that add up to 180˚

All straight angles form a line, therefore measure . Also, referred to as a linear pair.

CLASSIFYING TRIANGLES…

LET’S PRACTICE!

Complete #6-12 on the classwork. Be prepared to present and explain how you got your answers.

PARALLEL LINES

Parallel Lines: lines that do not intersect that are on the same plane

(to name parallel lines, you can use the symbol ||)

PARALLEL SEGMENTS

Example:

Name 2 parallel segments.

PARALLEL PLANESPLANES THAT DO NOT INTERSECT

Example:

Name a plane parallel to plane EGA.

NAMING AN ANGLEANGLE (): FORMED BY 2 RAYS WITH THE SAME ENDPOINT

To name an angle:

3 possible ways:

To indicate angle measure:

(angle measure in degrees)

DEFFED

E

,

1

Notice vertex is middle letter!

ANGLES WITH A SHARED VERTEX

Must name using a numbered angle or using 3 points with

vertex in the middle.

WARNING: Cannot write “ angle B”.

PARALLEL LINES CUT BY A TRANSVERSALWhen two parallel lines are cut by a transversal, sets and pairs of specific angles are created. Some of these angles have special characteristics.

PARALLEL LINES CUT BY A TRANSVERSALAlternate Interior Angles Non-adjacent

Lie on opposite sides of the transversal in between the 2 lines

Remember: interior means inside the parallel lines.

These angles are congruent!

Alternate Exterior AnglesLie outside the 2 lines on opposite sides of the transversal

These angles are congruent!

PARALLEL LINES CUT BY A TRANSVERSALSame-Side Interior AnglesLie on the same side of the transversal between the 2 lines

These angles are supplementary!

Same-Side Exterior Angles

Lie outside the 2 lines on same side of transversal

These angles are supplementary!

CORRESPONDING ANGLES Lie on the same side of the transversal

In corresponding (same) positions

These angles are congruent!

VERTICAL ANGLES

Vertical angles share the same vertex.

Vertical angles are congruent.

TIME TO PRACTICE!

Complete #13-15 with the person next to you. Be ready to put your answers on the board!

NICE WORK, MATHLETES!

GEOMETRY PRETEST REVIEW Day 3

SURFACE AREAIn words, the surface area of a rectangular prism is the area of the six rectangles that cover it.

But we don’t have to figure out all six sides because we know that the top and bottom are the same, the front and back are the same, and the left and the right sides are the same.

Example: Find the surface area of the box.

SA=2(lw)+2(hl)+2(hw)

VOLUME Volume=(length)(width)(height)

The amount of space occupied by a 3D figure as measured in cubic units (as inches, quarts, or centimeters)

Example: Find the volume of the box shown.

PROBABILITY

Example: Using the spinner, what is the probability of landing on an even number?

PRACTICE

Complete #16 and 17 from Worksheet #2.