Geometry Final Studysheet
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Special Right Triangles 45-45-90: •a = b •c = a√2 30-60-90: •b = a√3 •c = 2a 30° 60° 45° 45° cc a b b a c Euler’s formula : Faces + Vertices – Edges = 2 (for polyhedrons) Polyhedron : a geometric solid in three dimensions with flat faces and straight edges • Tetrahedron: four sides •Pentahedron: five sides •Hexahedron: six sides •Heptahedron: seven sides •Octahedron: eight sides etc… SOH-CAH-TOA sinθ = opposite/hypotenuse cosθ = adjacent/hypotenuse tanθ = Properties of Parallelograms •Both pairs of opposite sides are parallel •Both pairs of opposite sides are congruent •Both pairs of opposite angles are congruent •Diagonals bisect each other Properties of Rectangles •All properties of parallelograms •All diagonals are congruent •All angles measure 90 ° Properties of Rhombuses •All properties of parallelograms •All sides are congruent •All diagonals are perpendicular •All diagonals bisect opposite angles Properties of Squares •All properties of: •Parallelograms •Rectangles •Rhombuses Properties of Kites •The two diagonals are perpendicular •There are two pairs of congruent adjacent sides Angle of elevation Angle of depression
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A study sheet for high school Geometry
Transcript of Geometry Final Studysheet
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Special Right Triangles45-45-90:a = bc = a2
30-60-90:b = a3c = 2a
30604545ccabbacEulers formula: Faces + Vertices Edges = 2 (for polyhedrons)Polyhedron: a geometric solid in three dimensions with flat faces and straight edges Tetrahedron: four sidesPentahedron: five sidesHexahedron: six sidesHeptahedron: seven sidesOctahedron: eight sidesetcSOH-CAH-TOAsin = opposite/hypotenusecos = adjacent/hypotenusetan = opposite/adjacent6 Properties of ParallelogramsBoth pairs of opposite sides are parallelBoth pairs of opposite sides are congruentBoth pairs of opposite angles are congruentDiagonals bisect each otherProperties of Rectangles All properties of parallelogramsAll diagonals are congruentAll angles measure 90 Properties of RhombusesAll properties of parallelogramsAll sides are congruentAll diagonals are perpendicularAll diagonals bisect opposite anglesProperties of SquaresAll properties of:ParallelogramsRectanglesRhombusesProperties of KitesThe two diagonals are perpendicularThere are two pairs of congruent adjacent sides
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Regular Polygonsarea = (apothem*perimeter)one interior angle = ((n-2)180)/none exterior angle = 360/nwhere n = number of sides
Tangent-Tangent Angle Theorem: The measure of a tangent angle is equal to one half the measure of its two intercepted arcsTangent-Secant Angle Theorem: The measure of a tangent-secant angle is equal to one half the measure of its two intercepted arcsSecant-Secant Angle Theorem: The measure of a secant angle is equal to one half the difference of the measures of its two intercepted arcsm
- A tangent angle is the angle formed by two lines tangent to a circle. A
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Translation: a transformation that moves all points in a plane a fixed distance in a given directionVectors are used for translations to show the distance and direction of the translationRotation: a transformation in a plane or space that describes the motion of a rigid body around a fixed pointReflection: a transformation that creates a mirror image of an object which has point(s )equidistant to the line of reflection as the original objects point(s)
: describes a vector in the coordinate planeApply the vector to the coordinates of a point to translate it by the vectors dimensions
