Download Section 9.2 - Polygons

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Kendra
Kilmer May 25, 2008
Section 9.2 - Polygons
Definitions:
• A path that is drawn without picking up your pencil and without retracing any part of the path except
single points is known as a curve.
• A simple curve does not cross itself except the starting and stopping points may be the same.
• A closed curve can be drawn starting and stopping at the same point.
• Polygons are simple and closed and have sides that are line segments.
• A point where two sides of a polygon meet is a vertex.
• A curve is convex if it is simple, closed, and if a segment connecting any two points in the interior of
the curve is wholly contained in the interior of the curve. (i.e. there are no indentations)
• A concave curve is simple, closed, and not convex.
• A polygonal region includes the polygon and its interior.
Example 1: Classify each of the following figures:
Polygons are classifed according to the number of sides or vertices they have:
Number of Sides Name of Polygon
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Kendra
Kilmer May 25, 2008
More About Polygons:
• Any two sides of a polygon having a common vertex determine an interior angle.
• An exterior angle of a convex polygon is determined by a side of the polygon and the extension of a
contiguous side of the polygon.
• Any line segment connecting nonconsecutive vertices of a polygon is a diagonal of the polygon.
Congruent Segments and Angles:
• Two segments are congruent if a tracing of one line segment can be fitted exactly on top of the other
line segment.
• Two angles are congruent if they have the same measure.
• The symbol ∼
= is used to represent congruent.
• Polygons in which all the interior angles are congruent and all the sides are congruent are regular
polygons.
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Kendra
Kilmer May 25, 2008
Triangle Classifications:
• A triangle containing one right angle is a right triangle.
• A triangle in which all the angles are acute is an acute triangle.
• A triangle containing one obtuse angle is an obtuse triangle.
• A triangle with no congruent sides is a scalene triangle.
• A triangle with at least two congruent sides is an isosceles triangle.
• A triangle with three congruent sides is an equilateral triangle.
Quadrilateral Classifications:
• A trapezoid is a quadrilateral with at least one pair of parallel sides. (Note: Some elementary texts
define a trapezoid as a quadrilateral with exactly one pair of parallel sides.)
• A kite is a quadrilateral with two adjacent sides congruent and the other two sides also congruent.
• An isosceles trapezoid is a trapezoid with exactly one pair of congruent sides. (Equivalently, an isosceles trapezoid is a trapezoid with two congruent base angles.)
• A parallelogram is a quadrilateral in which each pair of opposite sides is parallel.
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Kendra
Kilmer May 25, 2008
• A rectangle is a parallelogram with a right angle. (Equivalently, a rectangle is a quadrilateral with four
right angles.)
• A rhombus is a parallelogram with two adjacent sides congruent. (Equivalently, a rhombus is a quadrilateral with all sides congruent.)
• A square is a rectangle with two adjacent sides congruent. (Equivalently, a square is a quadrilateral
with four right angles and four congruent sides.)
Example 2: Determine whether each of the following statements is true or false.
• An equilateral triangle is isosceles.
• A square is a regular quadrilateral.
• If one angle of a rhombus is a right angle, then all of the angles of the rhombus are right angles.
• A square is a rhombus with a right angle.
• All the angles of a rectangle are right angles.
• Some isosceles trapezoids are kites.
• If a kite has a right angle, then it must be a square.
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