Math176: Geometry Study Guide
Math176: Geometry Study Guide Math 176
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This 4 page Study Guide was uploaded by Emma Eiden on Saturday October 8, 2016. The Study Guide belongs to Math 176 at University of Wisconsin - Milwaukee taught by David Koslakiewicz in Fall 2016. Since its upload, it has received 60 views. For similar materials see Math Explorations for Elementary Teachers II in Mathematical Science at University of Wisconsin - Milwaukee.
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Date Created: 10/08/16
MATH176: MathematicalExploration forElementary Teachers II Study Guide: Test #1- Geometry (Wednesday, October12) Geometry-concernedwith theproperties andrelations of points,lines, surfaces, andhigher dimensionalanalogs When Adding Angles… Lines areinfinity long, no thickness, Two angles=90*(complementary) and thereare no end points Two angles=180*(supplementary) Lines can intersect and beparallel AcuteAngles 0-90* Right Angles 90* ObtuseAngle<90*, >180* Straight = 180* Right triangle AcuteTriangle ObtuseTriangle Triangle with aright angle All threeangles areless than Oneobtuseangle (morethan90*and othertwo angles are acute Quadrilaterals… - A foursided figure Parallelogram Rectangle Square Trapezoid Rhombus Kite Oppositeparallel sides Right Angles Right Angles, exactly one pair all sides equal all sides equal of equalsides no right angles two pairs of congruent sides Squares and rectangles are similar because they are both considered quadrilaterals but their definitions show they are very different shapes. Squares have right angles with all sides being congruent, while rectangles also have right angles, only two sides are congruent - TheDiameter thelongest cord in a circle - Area: A=πr2 (squared) Radius - Pi=3.14 Otherusefulterms… Reflex angle – An angle whose measure is greater than 180° degrees but less than Converse of a statement – In an if-then statement, the “if” and “then” are switched. Alternate interior angles – Given two parallel lines, angles that are in the interior and on opposite sides of a transversal. Corresponding angles - Given two parallel lines, angles that are on the same sideof a transversal and in corresponding positions. Exterior angle – An angle formed by extending the side of a triangle (polygon) Congruentangles – Angles that have the same measure. Perpendicular lines – Two lines that form 90 ̊ angles. Parallel lines – two lines in a plane that don’t meet. 12.2 Moving and Additivity Principles - Area Two fundamentalprinciples thatare used in determining thearea ofa shape TheMoving andAdditivity Principles MovingPrinciple–If youmoveashaperigidly withoutstretching it, then its area does notchange. AdditivityPrinciple–Ifyou combineafinite numberof shapeswithoutoverlapping them, then thearea of theresulting shapeis the sumof theareas of theindividual shapes. There are anumberofstrategies involving theseprinciples that willhelp us findthearea of ashape: Subdividetheshapeinto pieces whoseareas are easy to determine. Subdividetheshapeinto pieces, then moveand recombinethosepieces, without overlapping them,to makeanew shapewhosearea is easy to find. UsetheAdditivityPrinciple to “take away”area in orderto find thearea ofashape Pythagorean Theorem− Ina right triangle, thesquareof thelength of thehypotenuse(c)equals the sumof thesquares ofthe lengths ofthelegs (a, b).a2+ b2 =c2
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