# Geometry Review

 6.1 Basic Geometric figures 1) Segment 2) Ray 3) Line 1) A segment is a geometric figure consisting of two points called endpoints. 2) Ray Consists of a segment and all points between A and B and all points beyond b 3) Line Can consist of two rayes such as PQ and QP - can be named as a smaller letter mLines can be coplanar - Parrallel (l||m) or they can be intersecting 6.1 Basic Geometric Figures Angles 1) What is an Angle 2) Types of Angles 1) An Angle is a set of points consisting of two rays or half lines with a common end point, this end point is called a vertexUnit of Measure is degrees2) Types of Anglesa) Right angle = 90 degreesb)Acute angle - greater than 0 and less than 90 degreesc)Obtuse Angle - greater than 90 and less than 180 degreesd) Straight angle - measure is 180 degrees 6.1 Basic Geometric figures Perpendicular Lines Two lines a perpendicular if they intersect to form a right angle 6.1 basic Geometric figures - Polygons What are polygons? What are the most common polygons? 1) Polygons are shapes made up of 3 or more sides 6.1 Basic Geometric shapes - Triangles What is a triangle and what are the different types? 1) Triangles are polygons of 3 or more sides2) types of trianglesa)Equilateral Triangle - all sides same lengthb)Isosceles Triangle - two sides are the same lengthc)Scalane Triangle - All sides are of different lengthsd) right triangle - one angle is 90 degreese)Obtuse triangle - One angle is an obstuse angle between 90 and 180 degreesf)Acute triangle - all three angles are acute - less than 90 degrees 6.1 Basic Geometric figures - sum of angle measures for polygons 1)How do you find the sum of angles for more complex polygons? 2) What is the sum of angles for all triangles? 1)Take the number of sides (n) subtract 2 and multiply by 180 degrees(n-2)*180 degrees2) Sum of three angles in a triangle is 180 degrees 6.2 Perimeter og a polygon 1) What is perimeter? 2) Formulas for perimeter of a square and rectangle? 1) A polygons is a geometric figure with three or more sides. The perimeter of a polygon is the distance around it or the sum of length of its sides2) Perimeter of a rectangleP=2(l*w)3) SquareP=4*s 6.3 Area of Rectangles, Squares, parallelogram, triangle and trapezoid 1) Define area 2) Formulas for areas of various polygons 1) Area is defined as the measure of the interior form of a plane regionArea is expressed as squared - IE 5 sqr feet etcSquare units2) Common formulasRectangle - A=l.wSquare - A= s2Parellelogram - A = b*h (four sided figure with two pairs of parallel sides)Triangle A= 1/2*b*hTrapezoid A=1/2*h*(a+b) (polygon with 4 fours, two of which are bases which are parallel to each other 6.4 Circles - Radius, Diameter, Circumference and Area 1) Define each of Radius, Diameter and Circumference 2) Formulas for each Radius, Diameter and Circumference 1) Diameter - length across the circleRadius - length from center point to endCircumference - distance around the circle2)Diamter d = 2*rRadius r=d/2Circumference - when radius is knownC=2πrCircumference when Diameter is knownC=πdAreaA=πr2 6.5 Volume and Surface Area 1) Define formulas for Rectangule solid, circular cylinder, sphere and cone Volume is expressed as cubic units1) Rectangular Solids - Volcume is the number of unit cubes needed to fill itV=l*w*hSurface area of a rectangular solid - total area of the six rectangles that form the surface of the solidSA=2(lw+lh+wh)2) CylindersV=B*h or V=πr2 h3)SpheresV=4/3πr34)ConesV=1/3*B*h or V=1/3πr2 h 6.6 Relationships between Angle measures 1)Define complementary and supplementary angles 1)Two angles are complementary when the sum of their measures is 90 degresEach angle is said to complement of the otherThese are said to be acute angles - when they are adjacent they form a right angle2) Supplementary angles - angles are supplementary when the sum of the measure is 180 degreesEach angle is called the supplement of the other 6.6 Relationships between Angle measures - Congruency 1) define congruent angles and segments 1) Congruent segments - two segments that have the same length2) Congruent angles - angles that have the same measure 6.6 Relationships between Angle measures Vertical Angles 1) define what a vertical angle is 2)What is the vertical angle property? 1) two nonstraight angles are vertical angles if and only if their sides form two pairs of opposite raysAngles RPQ and SPT are called veritcal angles2) The vertical angle property - these angles are congruent 6.6 Relationships between Angle measures - Transversals and Angles 1) Define a transversal 2) what are the angle types formed? 1) A transversal is a line that intersects two or more coplanar lines in different pointsWhen a transversal intersects a pair of lines, eight angles are formed2) - Angle types formedCorresponding Angles - expressed in pairs <2 and <6, <3 and <7, <1 and <5, <4 and <8Interior angles - not expressed in pairs<3, <4,<5,<6Alternate Interior Angles - expressed as pairs<4 and <6, <3 and <5 6.6 Relationships between Angle measures Properties of Parralle Lines 1) In a transversal intersects two parallel lines, then the corresponding angles are congruent2) If a transversal intesects two parallel lines, then the alternate interior angles are congruent3) In a plane, if two lines are parallel to a third line, then the two lines are parallel to each other 4) if a tranversal intersects two parralel lines, then the interior angles on the same sideof the transversal are supplementary5) if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other 6.7 Congruent triangles and properties of parallelograms 1) Define Triangle types 2) Define the three properties to show why triangles are congruent 1) Classify triangles by their anglesAcute: All angles are acute ( less than 90 degrees)Right: One angle is a right angle ( 90 degrees)Obtuse: One obtuse angle ( greater than 90 degress less than 180 degreesEquiangular: all angles are congruent2) Classify triangles by their sidesEquilateral: All sides are congruentIsosceles - at least two sides are congruentScalane - No sides are congruent 3) Three properties to show why triangles are congruentTriangles are congruent if and only if their vertices can be matched so that the corresponding angles and sides are congruentCorresponding sides and angles of two congruent triangles are called corresponding parts of congruent trianglesCorresponding parts of congruent triangles are always congruentWe write to say that are congruentThe side-Angle-Side SAS propertyTwo triangles are congruent if two sides and the included angle of one triangle are congruent totwo sides and the included angle of the other triangle The Side-Side-Side (SSS) propertyIf three sides of one triangle are congruent to three sides of another trianglethen the triangles are congruent The Angle-Side-Angle (ASA) propertyIf two angles and the included side of a triangle are congruent to two angles and the included side of another triangle , then the triangles are congruent 6.7 Congruent triangles and properties of parallelograms Define the properties of parallelograms 1) A diagonal of a parallelogram determines two congruent triangles2) The opposite angles of a paralleogram are congruent3) The opposite sides of a paralleogram are congruent4) Consecutive angles of a parallelogram are suppelmentary5) Diagonals of a parallelogram bisect each other 6.8 Similar Triangles Review similar triangles Triangles can be similar to each other but not congruent in sizeTwo triangles are similar in and only if their vertices can be matched so that their corresponding angles are congruent and thelengths of corresponding sides are proportionalTo say that <>ABC and <>DEF are similar we write"<>ABC ~<>DEF"Thus, <>ABC ~ <>DEF means that Authortreborprime ID25558 Card SetGeometry Review DescriptionQLC1 Geometry review Updated2010-07-02T22:11:07Z Show Answers