Geometry: Polygons and Quadrilaterals

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.