Geometry: Polygons and Quadrilaterals
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Questions and Answers

What is the sum of the interior angles of a quadrilateral?

  • 360 degrees (correct)
  • 180 degrees
  • 540 degrees
  • 720 degrees

    • What is the measure of an exterior angle of a regular hexagon?

  • 30 degrees
  • 45 degrees
  • 60 degrees (correct)
  • 90 degrees

    • What is the name of a polygon with 5 sides?

  • Hexagon
  • Heptagon
  • Octagon
  • Pentagon (correct)

    • What is a characteristic of all polygons?

    <p>They consist of straight line segments with no curves.</p> Signup and view all the answers

    What is a type of quadrilateral with all sides congruent and opposite angles congruent?

    <p>Rhombus</p> Signup and view all the answers

    What is the sum of the interior angles of a triangle?

    <p>180 degrees</p> Signup and view all the answers

    What is a common characteristic of polygons?

    <p>They are two-dimensional shapes</p> Signup and view all the answers

    What is the name of a polygon with 3 sides?

    <p>Triangle</p> Signup and view all the answers

    What is the formula for the sum of interior angles of a polygon?

    <p>180(n-2)</p> Signup and view all the answers

    What is a characteristic of a square?

    <p>All sides are congruent, and all angles are equal</p> Signup and view all the answers

    What is the measure of an exterior angle of a regular octagon?

    <p>45 degrees</p> Signup and view all the answers

    What is the sum of interior angles of a heptagon?

    <p>900 degrees</p> Signup and view all the answers

    What is a characteristic of a trapezoid?

    <p>Two sides are parallel, and the other two sides are not parallel</p> Signup and view all the answers

    What is the sum of interior angles of a hexagon?

    <p>720 degrees</p> Signup and view all the answers

    What is a characteristic of a rhombus?

    <p>All sides are congruent, and opposite angles are congruent</p> Signup and view all the answers

    Study Notes

    Polygons

    • A polygon is a two-dimensional shape with straight sides and angles.
    • Examples of polygons:
      • Triangle (3-sided)
      • Quadrilateral (4-sided)
      • Pentagon (5-sided)
      • Hexagon (6-sided)
      • Heptagon (7-sided)
      • Octagon (8-sided)
      • Nonagon (9-sided)
      • Decagon (10-sided)

    Types of Quadrilaterals

    • Square: All sides are congruent, and all angles are equal to 90 degrees.
    • Rectangle: All angles are equal to 90 degrees, and opposite sides are congruent.
    • Trapezoid: Two sides are parallel, and the other two sides are not parallel.
    • Rhombus: All sides are congruent, and opposite angles are congruent.

    Characteristics of Polygons

    • Polygons are two-dimensional shapes.
    • Polygons are closed figures with no gaps or openings.
    • Polygons consist of straight line segments with no curves.
    • Polygons do not have intersecting lines.

    Sum of Interior Angles

    • The formula for the sum of interior angles is: 180(n-2), where n is the number of sides.
    • Examples:
      • Triangle (3-sided): 180(3-2) = 180 degrees
      • Quadrilateral (4-sided): 180(4-2) = 360 degrees
      • Pentagon (5-sided): 180(5-2) = 540 degrees
      • Hexagon (6-sided): 180(6-2) = 720 degrees
      • Heptagon (7-sided): 180(7-2) = 900 degrees
      • Octagon (8-sided): 180(8-2) = 1080 degrees

    Exterior Angles

    • The measure of an exterior angle of a regular polygon is: 360/n, where n is the number of sides.
    • Examples:
      • Triangle (3-sided): 360/3 = 120 degrees
      • Hexagon (6-sided): 360/6 = 60 degrees
      • Octagon (8-sided): 360/8 = 45 degrees

    Polygons

    • A polygon is a 2D shape with straight sides and angles.
    • Examples of polygons include triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, and nonagons.

    Types of Quadrilaterals

    • A square has congruent sides and 90-degree angles.
    • A rectangle has 90-degree angles and congruent opposite sides.
    • A trapezoid has two parallel sides and two non-parallel sides.
    • A rhombus has congruent sides and congruent opposite angles.

    Characteristics of Polygons

    • Polygons are 2D shapes.
    • Polygons are closed figures with no gaps or openings.
    • Polygons consist of straight line segments with no curves.
    • Polygons do not have intersecting lines.

    Sum of Interior Angles

    • The formula for the sum of interior angles is 180(n-2), where n is the number of sides.
    • The sum of interior angles of a triangle is 180 degrees.
    • The sum of interior angles of a quadrilateral is 360 degrees.
    • The sum of interior angles of a pentagon is 540 degrees.
    • The sum of interior angles of a hexagon is 720 degrees.
    • The sum of interior angles of a heptagon is 900 degrees.
    • The sum of interior angles of an octagon is 1080 degrees.

    Exterior Angles

    • The measure of an exterior angle of a regular polygon is 360/n, where n is the number of sides.
    • The measure of an exterior angle of a regular triangle is 120 degrees.
    • The measure of an exterior angle of a regular hexagon is 60 degrees.
    • The measure of an exterior angle of a regular octagon is 45 degrees.

    Polygons

    • A polygon is a 2D shape with straight sides and angles.
    • Examples of polygons include triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, and nonagons.

    Types of Quadrilaterals

    • A square has congruent sides and 90-degree angles.
    • A rectangle has 90-degree angles and congruent opposite sides.
    • A trapezoid has two parallel sides and two non-parallel sides.
    • A rhombus has congruent sides and congruent opposite angles.

    Characteristics of Polygons

    • Polygons are 2D shapes.
    • Polygons are closed figures with no gaps or openings.
    • Polygons consist of straight line segments with no curves.
    • Polygons do not have intersecting lines.

    Sum of Interior Angles

    • The formula for the sum of interior angles is 180(n-2), where n is the number of sides.
    • The sum of interior angles of a triangle is 180 degrees.
    • The sum of interior angles of a quadrilateral is 360 degrees.
    • The sum of interior angles of a pentagon is 540 degrees.
    • The sum of interior angles of a hexagon is 720 degrees.
    • The sum of interior angles of a heptagon is 900 degrees.
    • The sum of interior angles of an octagon is 1080 degrees.

    Exterior Angles

    • The measure of an exterior angle of a regular polygon is 360/n, where n is the number of sides.
    • The measure of an exterior angle of a regular triangle is 120 degrees.
    • The measure of an exterior angle of a regular hexagon is 60 degrees.
    • The measure of an exterior angle of a regular octagon is 45 degrees.

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