Classifying Quadrilaterals

Quadrilateral - Four sided figure.

Trapezoid - A quadrilateral with only one set ofparallel sides.

Parallelogram - A quadrilateral with two sets ofparallel sides.

Rectangle - A parallelogram with right angles.

Rhombus - A parallelogram with equal sides.Square - A rectangle with equal sides or a

rhombus with right angles.

Objective - To name different types of Polygons.

Quadrilateral

4 sided figure

TrapezoidOnly 1 setof parallel

sides

Isosceles Trapezoid

ParallelogramTwo sets

of parallelsides

RectangleParallel-ogram

with right angles

RhombusParallel-ogram

with equalsides

SquareRhombuswith right

angles

Rectanglewith equal

sides

State whether each statement is always true, sometimes true, or false.

1) A square is a rectangle.

2) A rectangle is a square.

3) All rectangles are squares.

4) All squares are parallelograms.

5) All quadrilaterals are rectangles.

6) A square is a trapezoid.

7) A parallelogram is a rectangle.

Always True

Sometimes True

False

Always True

False

False

Sometimes True

Make a Venn Diagram that accurately depictsthe relationships between quadrilaterals, trapezoids,parallelograms, rhombuses, rectangles, and squares.

Square RectangleRhombus

Parallelogram

Trapezoid

Quadrilaterals

Give all the names that apply to the figure below.Circle the most specific name.

1)

2)

3)

4)

Parallelogram, Quadrilateral

Trapezoid, Quadrilateral

6

10

6 6

8

14

7

7Quadrilateral, Parallelogram

, Rhombus

3 3

3 3

Quadrilateral, Parallelogram

Rectangle,

Rhombus,

, Square

What is a polygon?

Polygon - A closed figure made up of line segments.

Circle the polygons below.

Regular Polygon - Polygon with all sides congruentand all angles congruent.

Polygons

Polygons Regular PolygonsName# of sides Drawing NameDrawing

3 Triangle AcuteEquilateral

4 Quadrilateral Square

5 Pentagon RegularPentagon

6 Hexagon RegularHexagon

8 Octagon RegularOctagon

10 Decagon RegularDecagon

Convex vs. Concave(non-convex)

Convex - A polygon is convex if a segment connecting any two points withinthe figure is also fully containedwithin the figure.

cave

Convex Non-convex

Find the measure of each interior angle of a regular decagon.

Step 1 Find the sum of the interior angle measures.

Step 2 Find the measure of one interior angle.

(n – 2)180°

(10 – 2)180° = 1440°

Polygon Sum Thm.

Substitute 10 for n and simplify.

The int. s are , so divide by 10.

Example 4B: Finding Interior Angle Measures and Sums in Polygons

Find the value of b in polygon FGHJKL.

15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360°

Polygon Ext. Sum Thm.

120b = 360 Combine like terms.

b = 3 Divide both sides by 120.

Ann is making paper stars for party decorations. What is the measure of 1?

1 is an exterior angle of a regular pentagon. By the Polygon Exterior Angle Sum Theorem, the sum of the exterior angles measures is 360°.

A regular pentagon has 5 ext. , so divide the sum by 5.

1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex.

2. Find the sum of the interior angle measures of a convex 11-gon.

nonagon; irregular; concave

1620°

3. Find the measure of each interior angle of a regular 18-gon.

4. Find the measure of each exterior angle of a regular 15-gon.

160°

24°