Fundamentals of Geometry for Elementary School Teachers

"The space measured between two intersecting lines."Real Life Examples:Peice of wood cut at a 15 degree angle to make a stool for your kitchenCorner of a roomThe angle between the two intersecting cuts of one slice of pizzaThe corner of a brownie The corner of my book/paper

"Sum of two angels is 90 degrees."Real Life Examples:Park bench (two 45 degree angles)Sandwhich (sliced from one corner to any other end of the sandwhich)Two peices of pizza (from a full pizza cut into eight slices)Trick for Memorization:"C" for corner

"Sum of two angels is 180 degrees."Real Life Examples:Freeway entranceMy leg standing on top of the floorTwo slices of pizza from a pizza cut into foursThe letter tTrick for Memorization:"S" for straight

An angle of zero degrees where two lines lay on top of one another.

"Two lines on a plane that never meet and they are always the same distance apart because they have the same slope."Real life examples:Monkey BarsStreet yellow lines (when road is straight)Rail road tracksThe L's in the word parallel

An angle greater then zero degrees and less then 90 degrees.

An angle of 90 degrees, where two intersecting lines are perpendicular to one another.

"A line that meets or crosses another line at right angles (90 degrees).""Two lines that have opposite (negative reciprocal) slopes."Real Life Examples:A crossThe lower case letter " t "The sign people make with their arms when they call for a "timeout"

An angle greater then 90 degrees, but less then 180.

An angle that lies on a straight line. This angle can also be measured as 180 degrees.

An angle that is greater than 180 degrees, but less then 360. Often refered to in Layman's terms as the "outside" angle.

Chapter 11

Definitions/ ways to think about it:1.) "Using only one polygon to make 360 degrees at the vertex."2.) "Does to vertex of one polygon add up to 360 degrees?"/"Can the interior angle of the polygon be multiplied to equal 360 degrees?" If yes, then the tessellation is regular.3.) "The angles that meet at the vertex (using only one polygon) add up to 360."

A polygon is an enclosed shape with three or more sides, all of which are straight.A polygon can be concave or convex and the lines can cross one another.It is important to note that a polygon can approach the shape of a circle (with increased sides), but it can never actually become a circle because a polygon cannot have any curved lines.Real Life Examples:An arrowA stop signA TVFirst aid symbolA triangle

A convex polygon, both equilateral and equiangular.

All angles are congruent (same)

All sides are congruent (same).

"Equal in size or shape." Real Life Examples:Two of the same mugsIdentical twinsThe squares on a calendar

Where the lines of a polygon intersect one another.

"Formed by a rubber band stretched over the nails of a geoboard." Long, Calvin T., and Duane W. DeTemple. Mathematical Reasoning for Elemertary Teachers. Reading, MA: Addison-Wesley, 2000. Print.

Take the number of sides the polygon has and minus two. Then multiply this number by 180 degrees.ORTake the number of sides the polygon has and multiply it by 180, then subtract 360 from the total.

three-sided polygons

A triangle that has all acute angles within.

A triangle with and obtuse angle within it.

A triangle with a right angle within it.

A triangle with all equal sides/angles.

A triangle with two egual sides and two of the same angles.

A triangle with no two sides of equal length (no equal angles)

four-sided polygons

TEXTBOOK DEFINITION: a quadrilateral with at least on pair of parrellel sides.Note: Some dictionaries and text require a trapezoid to have exactly one pair of parallel sidesMathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.

TEXTBOOK DEFINITION: A trapezoid with a Mathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.

TEXTBOOK DEFINITION: A parallelogram with a right angle.Mathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.

A rectangle with all sides of equal length.

TEXTBOOK DEFINITION: a parallelogramMathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.Note: An Equiangular Rombus is a Square.

TEXTBOOK DEFINITION: A quadrilateral in which each pair of opposite sides is parallel.Mathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.

TEXTBOOK DEFINITION: A quadrilateral with two distinct pairs of congruent adjacent sides. A kite can be either convex or concave.Mathematical Reasoning for Elementary School Teachers. N.p.: Addison-Wesley, 2011. Print.

polygon with five sides

polygon with six sides

polygon with seven sides

A three - dimensional figure made up of sides called faces, each face being a polygon (polygonal regions).Other Parts of a Polyhedra:Vertices then corners, or where the lines/rays/edges meetEdges the sides of each polygon

The point at which every triangle arising from the base meets.

("n" being the n-gon of the base)Also note: There are always 4 or more triangles

Ask yourself two questions:1.) Is is "right" or "oblique"? -It is RIGHT if you drew a line segment from the apex to the center of the base and this created a 90 degree angle. -Otherwise, it is OBLIQUE*Another way to think of this question: Is the pyramid slanted/tilted or straight? If it is straight, it is RIGHT. If it is slanted, it is OBLIQUE2.) What polygon is the base?Example of name: The Egyption Pyramids would be "right, square pyramids."

Two congruent polygons, which are parallel planes (called bases), and the lateral faces joining the bases, which are parallelograms.

"A side part of something"Example: The roots of a plant are lateral

Ask yourself these three questions:1.) Is is convex or concave (nonconvex)? 2.) Is it "right" or "oblique"? At what angles do the faces meet the base?-If the faces are rectangles and they meet at a 90 degree angle, then the prism is called RIGHT.-Otherwise, it is called OBLIQUE*Another way to think of this question: Is the pyramid slanted/tilted or straight? If it is straight, it is RIGHT. If it is slanted, it is OBLIQUE.3.) What polygon is the base?Example: A nonconvex, right, pentigonal prism.

(often circular)

At what angle does the line segment between the apex and the center of the base meet?

(often circular, always congruent)

At what angle does the line segment between the center of the top base and the center of the bottoem base meet?

"A straight line which links two points without extending beyond them." ("Line Segment Definition - Math Open Reference." Line Segment Definition - Math Open Reference.)"A straight line that begins and ends."Real Life Examples:One side of a door frameOne side of a rulerOne side of your TV

"The commen point of two or more rays or line segments.""The ultimate high or low point of two intersecting lines."Real Life Examples:The bottom of the letter UThe bottom of the letter V in VertexThe base of a hand-held fan*Plural Word: "Vertices"

"A line that starts at a point with given coordinates, and goes off in a particular direction to infinity, possiably through a second point." ("Ray Definition (Coordinate Geometry) - Math Open Reference." Ray Definition (Coordinate Geometry) - Math Open Reference. N.p., n.d. Web)"A straight line that begins, but never ends."Real Life Example:Sun rays