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Chapter 11 Study Guide

by: Clarendon Notetaker

Chapter 11 Study Guide MTED 211

Clarendon Notetaker
Long Beach State

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About this Document

Everything we've covered in Chapter 11: formulas/equations for polygons, triangles, circles, and angles!
Mathematics Education Geometry
Rebekah Moule
Study Guide
Math, triangle, circle, angle, polygon, 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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