GEOMETRY PRETEST REVIEW Reviewing skills needed to succeed in Geometry. Day 1

REDUCING FRACTIONS 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

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.

SOLVING PROPORTIONS ad = bc

THE COORDINATE PLANE

SLOPE  Slope measures how steep a line is.  There are 4 kinds of slope.  To find the slope between 2 points on a line:

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 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 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.

#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. #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 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: in 2, cm 2, mi 2, 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 = 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 a 2 + b 2 = c 2

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

VOCABULARY

EXAMPLES 2. A BABC 1. Read “segment AB” or “segment BA” 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 above What are “opposite rays”?

PLANES  A 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 ANGLES Complementary angles: 2 angles that add up to 90˚ Supplementary angles: 2 angles that add up to 180˚

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 PLANES PLANES THAT DO NOT INTERSECT Example: Name a plane parallel to plane EGA.

To name an angle: 3 possible ways:  To indicate angle measure: Notice vertex is middle letter!

ANGLES WITH A SHARED VERTEX

PARALLEL LINES CUT BY A TRANSVERSAL When 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 TRANSVERSAL Alternate 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 Angles  Lie outside the 2 lines on opposite sides of the transversal  These angles are congruent!

PARALLEL LINES CUT BY A TRANSVERSAL Same-Side Interior Angles  Lie 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 AREA In 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.