Chapter 11 Study Guide
Chapter 11 Study Guide MTED 211
Long Beach State
Popular in Mathematics Education Geometry
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This 3 page Study Guide was uploaded by Clarendon Notetaker on Thursday February 4, 2016. The Study Guide belongs to MTED 211 at California State University Long Beach taught by Rebekah Moule in Spring 2016. Since its upload, it has received 39 views.
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Date Created: 02/04/16
To calculate how many lines can be drawn through n amount of points: n (n1) / 2 = Types of angles: Acute: < 90° Obtuse: > 90° Right: 90° Adjacent: angles that share a common vertex and a common side, but their interior angles do not overlap Consecutive: 2 interiorangles lying on the same side of the transversal cutting across two parallel lines; parallel lines cut by a transversal Supplementary: 2 angles whose sum is 180° Complementary: 2 angles whose sum is 90° = Angles of Measurement: Degree: 1/360 of a rotation about a point; ° Minute: 1/60 of a ° ; ‘ Second: 1/60 of a ‘ ; “ = Curves and Polygons: Simple: does not intersect itself Closed: starts and stops at the same point Polygons: simple closed curves with only segments as sides Vertex: the point where two sides (of a polygon) meet Convex: curves are simple and closed, such that the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve; no indentations Concave: curves are simple, closed, and not convex; has an indentation = Types of triangles: Right, acute, obtuse (refer to angles above) = Scalene: no congruent sides Isosceles: at least two congruent sides Equilateral: all sides are congruent = Trapezoid: quadrilateral with only one pair of parallel sides Kite: quad. with 2 congruent, adjacent sides & the other 2 also congruent Isosceles trapezoid: trapezoid with congruent base angles Parallelogram: quad. where both pairs of opposite sides are parallel and equal in length Rectangle: parallelogram with 4 right angles Rhombus: parallelogram with all sides the same length Square: a rectangle with all sides the same length = Triangle inequality: the sum of the lengths of only two sides of a triangle is greater than the length of the 3rd, longest side = Circumference: 2πr or πd To calculate the arc length ℓ: θ/360° (2πr) = 2πrθ/360 = πrθ/180 Types of Polygons: 3: Triangle 4: Quadrilateral 5: Pentagon 6: Hexagon 7: Heptagon 8: Octagon 9: Nonagon 10: Decagon 12: Dodecagon n: ngon = Regular Polygon: ALL sides are congruent, ALL angles are congruent = equilateral and equiangular Interior angle or Interior vertex angle: an angle formed by 2 sides of a polygon with a common vertex Angle sum of a polygon: the sum of the interior/vertex angles of a polygon Exterior angle of a convex polygon: an angle formed by a side of a polygon and the extension of a continuous side of the polygon an interior angle and exterior angle of a convex polygon will add up to 180° Diagonal: a line segment connecting nonconsecutive vertices of a polygon = Symmetry: a characteristic of shape; visual balance Reflectional or Line: line of symmetry where both sides mirror each other; a geometric figure has a line of symmetry, ℓ, if it is its own image folded along the line ℓ Rotational or Turn: when the traced figure can be rotated less than 360° about some point, the turn center, so that it matches the original figure to find rotational symmetry: take the amount of degrees (360) and divide it by the amount of points Point: a type of rotational symmetry at exactly 180° a figure can have all 3 types of symmetry = More about angles: Vertical angles: created by intersecting lines, pair of angles whose sides are two pairs of opposite rays; the angles are congruent Refer to image: Interior angles: <3, <4, <5, and <6 Exterior angles: <1, <2, <7, and <8 Alternate interior angles are pairs: <3 and <6, <4 and <5 Alternate exterior angles are pairs: <1 and <8, <2 and <7 Corresponding angles are pairs: <1 and <5, <2 and <6, <3 and <7, <4 and <8 The sum of the measures of the interior angles of any convengon is (n2)180° The sum of the measures of the exterior angles of any convengon is 360° = If, then statements: If 2 lines cut by a transversal… are parallel, then the corresponding angles are congruent are parallel, then their alternate exterior/ interior angles are congruent are parallel, then their obtuse angles/their acute angles are congruent and the corresponding angles are congruent, then the lines are parallel = To find the sum of the measures of the angles ngon: n•180° 360° The sum of the measures of the interior angles of any convengon: (n2)180° The sum of the measures of the exterior angles of any convengon is 360°
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