Questions and Answers
What is a polygon?
What defines a quadrilateral?
It is a 4-sided polygon.
A parallelogram has only one pair of opposite sides that are parallel.
False
How many pairs of opposite sides are parallel in a trapezoid?
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A kite has parallel sides.
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What is an isosceles trapezoid?
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What are the characteristics of a rectangle?
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What is a rhombus?
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A square has diagonals that are perpendicular.
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The sum of the interior angles of a polygon with n sides is given by the formula S = (n - 2) x 180. Here, S stands for the ______ of interior angles.
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What is the sum of the exterior angle measures of a convex polygon?
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How many sides does a pentagon have?
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What is the definition of a hexagon?
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How many sides does a heptagon have?
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What is an octagon?
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How many sides does a nonagon have?
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What defines a decagon?
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A regular polygon has sides of unequal lengths.
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An irregular polygon has equal side lengths.
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What is a concave polygon?
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Define a convex polygon.
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Study Notes
Polygon Basics
- A polygon is a closed figure with straight sides.
- Quadrilaterals are polygons that specifically have four sides.
Types of Quadrilaterals
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Parallelogram
- Has one pair of opposite sides that are both parallel and congruent.
- Features two pairs of parallel sides, congruent opposite sides, congruent opposite angles, supplementary consecutive angles, and diagonals that bisect each other.
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Trapezoid
- Defined by having exactly one pair of opposite sides that are parallel.
- Consecutive angles between different bases are supplementary.
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Kite
- Characterized by having no parallel sides.
- Contains two pairs of congruent consecutive sides, perpendicular diagonals, one pair of congruent opposite angles, and a bisecting diagonal that divides it into two congruent triangles.
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Isosceles Trapezoid
- Has congruent legs and congruent angles at the bases.
- Diagonals are also congruent.
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Rectangle
- A parallelogram with four right angles leading to four congruent angles.
- Diagonals are congruent.
-
Rhombus
- A quadrilateral with four congruent sides and perpendicular diagonals.
- Diagonals bisect opposite angles.
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Square
- Combines properties of a rectangle and rhombus: all angles are right, all sides are congruent, and diagonals are both perpendicular and congruent.
Angle Theorems
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Interior Angles Theorem
- The sum of a polygon’s interior angles is calculated with the formula S = (n-2) x 180, where n is the number of sides.
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Exterior Angles Theorem
- The sum of exterior angles of a convex polygon equals 360 degrees, with one at each vertex.
Polygons by Sides
- Pentagon: 5 sides
- Hexagon: 6 sides
- Heptagon: 7 sides
- Octagon: 8 sides
- Nonagon: 9 sides
- Decagon: 10 sides
Polygon Types
- Regular Polygon: All sides are equal in length and all angles are equal.
- Irregular Polygon: Sides are of unequal lengths.
- Concave Polygon: At least one angle points inwards.
- Convex Polygon: All angles point outwards, with no angles pointing inwards.
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Description
This quiz focuses on key terms related to polygons and quadrilaterals as covered in Geometry Chapter 6. Review essential definitions and characteristics of various shapes like parallelograms. Perfect for reinforcing your understanding of geometric concepts.
