Polygons Not Polygons What is the definition of

Polygons Not Polygons

What is the definition of a polygon? Answer A closed flat figure with at least three straight sides

Polygons Definition: A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons These figures are polygons 4

Classifications of a Polygon Convex: No line containing a side of the polygon contains a point in its interior Concave: A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon. 5

Classifications of a Polygon Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular: Two sides (or two interior angles) are not congruent. 6

Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon 12 sides Dodecagon n sides n-gon 7

Regular Polygons • Regular polygons have: • All side lengths congruent • All angles congruent 8

Quadrilaterals Not Quadrilaterals

What is the definition of a quadrilateral? Answer A polygon with four sides

What is a Quadrilateral? • All quadrilaterals have four sides. • They also have four angles. • The sum of the four angles totals 360° • These properties are what make quadrilaterals alike, but what makes them different?

Parallelograms Not Parallelograms

What is the definition of a parallelogram? Answer A quadrilateral with two pairs of parallel sides

Parallelogram • Two sets of parallel sides • Two sets of congruent sides. • The angles that are opposite each other are congruent (equal measure).

Rectangles Not Rectangles

What is the definition of a rectangle? Answer A quadrilateral with four right angles and two pairs of parallel sides

Rectangle • Has all properties of quadrilateral and parallelogram • A rectangle also has four right angles. • A rectangle can be referred to as an equiangular parallelogram because all four of it’s angle are right, meaning they are all 90° (four equal angles).

Square Not Squares

What is the definition of a square? Answer A quadrilateral with four right angles, two pairs of parallel sides, and all sides equal

Square • The square is the most specific member of the family of quadrilaterals. The square has the largest number of properties. • Squares have all the properties of a quadrilateral, all the properties of a parallelogram, all the properties of a rectangle, and all the properties of a rhombus. • A square can be called a rectangle, rhombus, or a parallelogram because it has all of the properties specific to those figures.

Rhombus Not Rhombus

What is the definition of a rhombus? Answer A quadrilateral with two pairs of parallel sides and all sides equal

Rhombus • A rhombus is sometimes referred to as a “slanted square”. • A rhombus has all the properties of a quadrilateral and all the properties of a parallelogram, in addition to other properties. • A rhombus is often referred to as a equilateral parallelogram, because it has four sides that are congruent (each side length has equal measure).

Trapezoids Not Trapezoids

What is the definition of a Trapezoid? Answer A quadrilateral with exactly one pairs of parallel sides

Isosceles Trapezoid • One can never assume a trapezoid is isosceles unless they are given that the trapezoid has specific properties of an isosceles trapezoid. • Isosceles is defined as having two equal sides. Therefore, an isosceles trapezoid has two equal sides. These equal sides are called the legs of the trapezoid, which are the non-parallel sides of the trapezoid. • Both pair of base angles in an isosceles trapezoid are also congruent.

Right Trapezoid • A right trapezoid also has one set of parallel sides, and one set of non-parallel sides. • A right trapezoid has exactly two right angles. This means that two angles measure 90°. • There should be no problem identifying this quadrilateral correctly, because it’s just like it’s name. When you think of right trapezoid, think of right angles!

What is the definition of a regular polygon? Equilateral triangle Answer What do we call a regular triangle? What do we call a regular quadrilateral? Square A polygon with all sides and angles congruent

Classify each quadrilateral in as many ways as possible by dragging the terms and placing them on top of the shape. Terms may be used more than once. trapezoid quadrilateral 4. 1. square rhombus parallelogram quadrilateral rectangle rhombus quadrilateral parallelogram 2. trapezoid square quadrilateral 3. parallelogram rectangle quadrilateral parallelogram rectangle rhombus

Quadrilateral Family Tree It’s important to have a good understanding of how each of the quadrilaterals relate to one another. Quadrilateral Parallelogram Rectangle Trapezoid A rectangle and rhombus are both types of parallelograms, and a square can be considered a rectangle, rhombus, and a parallelogram. Rhombus Square Any quadrilateral that has two sets of parallel sides can be considered a parallelogram. Isosceles Right Trapezoid Any quadrilateral that has one set of parallel sides is a trapezoid. Isosceles and Right are two types of trapezoids.

Sum of the Interior Angles of a Quadrilateral If you draw a diagonal of a quadrilateral, you will get two triangles. 1. ) Use this information to find the sum of the interior angles of this quadrilateral. The sum of the angles of a quadrilateral is 360.

Student Activity #1 • Place your 16 quadrilaterals in front of you • Draw a Venn. Diagram on your whiteboard. • Sort your quadrilaterals on the Venn. Diagram

Student Activity #2 • Create the Venn. Diagrams based on the two shapes you are given • Figure out which label would fit each ring for each Venn. Diagram. • Explain your reasoning.