Tuesday, April 1, 2008

Notes For March 26th
Theorem 8-17: If the diagonals of a parallelogram bisect the opposite angles of the parallelogram then the parallelogram is a rhombusSummary Rhombi1) A rhombus has all the properties of a parallelogram.2) All sides are congruent3) Diagonals are perpendicular4)Diagonals bisect the angles of the rhombusSummary Squares1) A square has all the properties of a parallelogram2) A square has all of the properties of the rectangle3) A square has all of the properties of the rhombusTrapezoidWhat is a trapezoid?A trapezoid is a quadrilateral with exactly one set of parallel sidesTrapezoid Bases: The parallel sides of the trapezoid.Trapezoid Legs: The non-parallel sides of a trapezoidIsosceles Trapezoid: If the legz of a trapezoid are congruent then the trapezoid is isoceles.Median of a trapezoid- Is the segment that connects the medpoints of the legs of a trapezoid.Theorems, Postulates, & Definitions
· Theorem 8-18: Both pairs of base angles of an isosceles trapezoid are congruent
· Theorem 8-19: The diagonals of an isosceles trapezoid are congruent.
pages434-43512-34

Math Notes March 6, 2008Polygon Angle Sum TheoremsObjectives:· To Classify Polygons· To find the sum of the measures of the interior and exterior angles.Polygon:· A closed plane figure.· With at least 3 sides (segments)· The sides only intersect at their endpoints· Name it by starting at a vertex & go around the figure clockwise or counterclockwise listing each vertex you come across.Example one:II. Also Classify polygons by their shapea) Convex Polygon: Has no diagonalWith points outside the polygon.b) Concave Polygon: Has at leastOne diagonal with points outside the polygon.a)
Math Notes March 11, 2007Using a calculator will give you an approximation.

· Math Notes;· Check to see if it is a rectangle as well as a rhombus:· W(1,10); X(-4,0); Y(7,2); Z(12,12)· The diagonals are not congruent, so this is not a rectangle or a square.

· Math Notes;· Check to see if it is a rectangle as well as a rhombus:· W(1,10); X(-4,0); Y(7,2); Z(12,12)· The diagonals are not congruent, so this is not a rectangle or a square
Geom Notes For SQUARE ROOTS! ;]
RootsSquare RootsWhen working a square root problem. Ask: -- what times itself is the number inside the root symbol?”=3 because 3 times 3 is 9because 5 times 5 is 25Roots and Prime Numbers=3 because 3x3x3 is 27. The small 3 outside the root symbol tells how many times the answer must be multiplied to get the number inside the root.because 2x2x2x2x2 or 25=32Prime Number: a number with only factor one and itself 2,3,5,7,9,11,13,1,7,19,23… are prime numbers fifteen is not prime because 3 and 5 also divide it evenly. 15 is a composite number.Prime factorization.Prime Factorization is writing a number using multiplication of only prime numbers.12 can be written as 3x4 but 4 is not prime and can be written as 2x2So the prime factorization of 12 is 3x2x2 this can also be written 3x22Graphing Prime Numbers33010 x 335 x2 3 x 11To write 330 using its prime factorization start breaking it down by each number.Simplifying RootsYou won’t be using the radical button on your calculator anymore.= 2Prime Factorization
Definition- RectangleA rectangle is a parallelogram with four right angles.PROPERTIES1. Opposite sides are congruent and parallel.2. Opposite angles are congruent.3. Consecutive angles are supplementary.4. Diagonals bisect each other and are congruent.5. All four angles are right angles.Theorems, Postulates, & definitions.Theorem 8-13: If a parallelogram is a rectangles the diagonals are congruent.Note: If one angle of a parallelogram is a right angle then the parallelogram is a rectangle.The Housebuilder Theorem 8-14: If the diagonals of a parallelogram are congruent then the parallelogram are congruent then the parallelogram is a rectangle.Rhombi and SquaresTheorem 8-15: The diagonals of a rhombus is perpendicular.Theorem 8-16: If the diagonals of a parallelogram are perpendicular then the parallelogram is a rhombus.

Theorems, Postulates, and Definitions.Theorem 8-8: If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.Theorem 8-10: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.Theorem 8-11: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.Theorem 8-12: If one pair of opposite sides of a quadrilateral are parellel and congruent, then the quadrilateral is a parrelellagram.
Summary!
A quadrilateral is a parallelogram if any one of the following statements are true.1. Both pairrs of opposite sides are parrallel. (definition)2. Both pairs of opposite sides are congruent. (theorem 8-9)3. Both pairs of opposite angles are congruent (throrem -10)4. The diagnols bisect each other (theorem 8-11)5. A pair of opposite sides is both parellel and congruent (theorem 8-12)
Parallelograms in the coordinate plane
The slope formula can be used to determine if the opposite sides have the same slope.
The distance formula can be used to see if the opposite sides are congruent or
The slope and the distance formula ccan be used to determine if one pair of opposite sides is parallel and congruent.

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