Classifying Quadrilaterals Quadrilateral -Four sided figure. Trapezoid -A quadrilateral with only...
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Transcript of Classifying Quadrilaterals Quadrilateral -Four sided figure. Trapezoid -A quadrilateral with only...
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°