21

Exploring Polygons

Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Download PPT Report

Upload
gertrude-porter
View
228
Download
2

Tags:

Embed Size (px)

Citation preview

Page 1: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Exploring Polygons

Page 2: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

What are polygons?

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

The following are examples of polygons:

Page 3: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

The figures below are not polygons. Can you tell why?

Page 4: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Regular Polygons

A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.

The following are examples of regular polygons:

Would a square be a regular polygon? A rectangle?

Page 5: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

The following are not examples of regular polygons:

How do you know?

Page 6: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

TrianglesAll three-sided polygons.

There are many special types of triangles.

Page 7: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

QuadrilateralA four-sided polygon.

Page 8: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Angles in quadrilaterals…Quadrilaterals have four sides and four angles.

The sum of the measures of the angles is 360°.

Find the value of x in the quadrilateral below

x° + 105° + 80° + 95° = 360°

Add 105°, 80°, and 95°.

x° + 280° = 360°

THINK: What measure

added to 280° equals 360°?

80° + 280° = 360°

x° = 80°

Page 9: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Find the value of x in each quadrilateral.

Page 10: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

A rectangle has opposite sides congruent and parallel, and all right

angles.

Are rectangles a kind of quadrilateral?

How do you know?

Page 11: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

A square has all sides congruent, opposite sides parallel, and all right

angles.

Are squares a kind of rectangle?

How do you know?

Page 12: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

A parallelogram has opposite sides congruent and parallel, and opposite

angles congruent.

Are parallelograms a kind of rectangle? How do you know?

Page 13: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

A rhombus has all sides congruent, opposite sides parallel, and opposite

angles congruent.

How are rhombuses and squares similar? How are rhombuses and squares different?

Page 14: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

A trapezoid has exactly one pair of opposite sides parallel.

There are special types of trapezoids ….that’s for another day!

Page 15: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

Classify each quadrilateral.

Page 16: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

PentagonA five-sided polygon

a regular pentagon

an irregular pentagon

Page 17: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

HexagonA six-sided polygon.

a regular hexagon

an irregular hexagon

Page 18: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

HeptagonA seven-sided polygon

A regular heptagon

an irregular heptagon

Page 19: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

OctagonAn eight-sided polygon.

A regular octagon

An irregular octagon

Page 20: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

NonagonA nine-sided polygon.

A regular nonagon

An irregular nonagon

Page 21: Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others

DecagonA ten-sided polygon.

A regular decagon

An irregular decagon

A line that intersects two or more lines. Transversal

A line that intersects two or more lines. Transversal

Documents

POLYGONS - Weeblyepvteror.weebly.com › uploads › 5 › 2 › 0 › 2 › 5202576 › _ud1_part2_polygons.pdfPOLYGONS Polygons are many-sided figures, with sides that are line segments

POLYGONS - Weeblyepvteror.weebly.com › uploads › 5 › 2 › 0 › 2 › 5202576 › _ud1_part2_polygons.pdfPOLYGONS Polygons are many-sided figures, with sides that are line segments

Documents

INTERSECTIONS OF LINE SEGMENTS AND POLYGONS · Felkel: Computational geometry Line segment intersection - Sweep line alg. Avoid testing of pairs of segments far apart Compute intersections

INTERSECTIONS OF LINE SEGMENTS AND POLYGONS · Felkel: Computational geometry Line segment intersection - Sweep line alg. Avoid testing of pairs of segments far apart Compute intersections

Documents

WHAT IS A POLYGON? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. The following

WHAT IS A POLYGON? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. The following

Documents

Polygons - computergraphics2015.files.wordpress.com fileAgenda Polygon Terminology Types of polygons Inside Test Polygon Filling Algorithms Scan-Line Polygon Fill Algorithm Flood-Fill

Polygons - computergraphics2015.files.wordpress.com fileAgenda Polygon Terminology Types of polygons Inside Test Polygon Filling Algorithms Scan-Line Polygon Fill Algorithm Flood-Fill

Documents

3.2 More Neutral Theorems Pasch’s Axiom-If a line l intersects Δ PQR at point S such that P-S-Q, then l intersects Crossbar Theorem-If X is a point in

3.2 More Neutral Theorems Pasch’s Axiom-If a line l intersects Δ PQR at point S such that P-S-Q, then l intersects Crossbar Theorem-If X is a point in

Documents

Warm Up · 2013. 10. 9. · Angles and Transversals.notebook 2 October 08, 2013 t l m Transversal Transversal: A line that intersects two or Note: The lines the transversal intersects

Warm Up · 2013. 10. 9. · Angles and Transversals.notebook 2 October 08, 2013 t l m Transversal Transversal: A line that intersects two or Note: The lines the transversal intersects

Documents

CE 597 Spring 2011. Point Line Polygon Thematic collections of points, lines, or polygons

CE 597 Spring 2011. Point Line Polygon Thematic collections of points, lines, or polygons

Documents

8.1 Classifying Polygons. Polygon Review Characteristics of a Polygon All sides are lines Closed figure No side intersects more than 1 other side at

8.1 Classifying Polygons. Polygon Review Characteristics of a Polygon All sides are lines Closed figure No side intersects more than 1 other side at

Documents

1. What forms the sides of both regular and irregular polygons? line segments

1. What forms the sides of both regular and irregular polygons? line segments

Documents

Application of Derivative - 1 Meeting 7. Tangent Line We say that a line is tangent to a curve when the line touches or intersects the curve at exactly

Application of Derivative - 1 Meeting 7. Tangent Line We say that a line is tangent to a curve when the line touches or intersects the curve at exactly

Documents

1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Documents

Polygon Review - educationmathmodule.ua.edu filePolygon A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. Examples:

Polygon Review - educationmathmodule.ua.edu filePolygon A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. Examples:

Documents

$The hyperboloid model of hyperbolic geometry · 2020. 5. 13. · Coxeter gives Proclus’s assumtion as \If a line intersects one of two parallels, it also intersects the other"$

The hyperboloid model of hyperbolic geometry · 2020. 5. 13. · Coxeter gives Proclus’s assumtion as \If a line intersects one of two parallels, it also intersects the other"

Documents

Definition of Perpendicular lines (IMPORTANT): Two lines that intersect to form RIGHT ANGLES! A line perpendicular to a plane is a line that intersects

Definition of Perpendicular lines (IMPORTANT): Two lines that intersect to form RIGHT ANGLES! A line perpendicular to a plane is a line that intersects

Documents

9-2 Polygons More About Polygons Congruent Segments and Angles Regular Polygons Triangles and Quadrilaterals Hierarchy Among Polygons

9-2 Polygons More About Polygons Congruent Segments and Angles Regular Polygons Triangles and Quadrilaterals Hierarchy Among Polygons

Documents

POLYGONS. Polygon : a closed figure formed by coplanar line segments such that: − segments with a common endpoint are non-collinear − each segment intersects

POLYGONS. Polygon : a closed figure formed by coplanar line segments such that: − segments with a common endpoint are non-collinear − each segment intersects

Documents

PASS REVIEW 3 rd Grade Math Review. POLYGONS A polygon is a plane figure that is closed with thee or more line segments. Polygons are classified based

PASS REVIEW 3 rd Grade Math Review. POLYGONS A polygon is a plane figure that is closed with thee or more line segments. Polygons are classified based

Documents

1 What is a polygon? a closed figure made by joining line segments Each line segment intersects exactly two others. line segments do not intersect *All

1 What is a polygon? a closed figure made by joining line segments Each line segment intersects exactly two others. line segments do not intersect *All

Documents

What is a tangent? A tangent (Line AB) is a line that intersects the outside of the circle. The point of tangency (Point P) is where the line intersects

What is a tangent? A tangent (Line AB) is a line that intersects the outside of the circle. The point of tangency (Point P) is where the line intersects

Documents

5/17/2015 Geometry Section 6.1 Polygons. Polygon 1. A plane figure formed by three or more segments called sides. 2. Each side intersects exactly two

5/17/2015 Geometry Section 6.1 Polygons. Polygon 1. A plane figure formed by three or more segments called sides. 2. Each side intersects exactly two

Documents

EVERYDAYEVERYDAY. A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. Polygon

EVERYDAYEVERYDAY. A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. Polygon

Documents

VC)lu11:l:e~O:·'arl2 - QEDCAT · which is equivalent to x = c or (x·-a)2 + b2~. m =O. The line intersects The line intersects the cubic only twice, so this last quadratic equation

VC)lu11:l:e~O:·'arl2 - QEDCAT · which is equivalent to x = c or (x·-a)2 + b2~. m =O. The line intersects The line intersects the cubic only twice, so this last quadratic equation

Documents

Which angles are linear pairs?. Quiz Tomorrow A line that intersects two lines at two points When a transversal intersects parallel lines, it creates

Which angles are linear pairs?. Quiz Tomorrow A line that intersects two lines at two points When a transversal intersects parallel lines, it creates

Documents

POLYGONS - Weeblyepvteror.weebly.com/uploads/5/2/0/2/5202576/_unit5_polygons.pdf · POLYGONS Polygons are many-sided figures, with sides that are line segments. The word polygon is

POLYGONS - Weeblyepvteror.weebly.com/uploads/5/2/0/2/5202576/_unit5_polygons.pdf · POLYGONS Polygons are many-sided figures, with sides that are line segments. The word polygon is

Documents

INTERSECTIONS OF LINE SEGMENTS AND POLYGONS · INTERSECTIONS OF LINE SEGMENTS AND POLYGONS ... Intersections of line segments ... – log n search the status tree

INTERSECTIONS OF LINE SEGMENTS AND POLYGONS · INTERSECTIONS OF LINE SEGMENTS AND POLYGONS ... Intersections of line segments ... – log n search the status tree

Documents

Exploring. Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have

Exploring. Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have

Documents

CS4522 Advanced Algorithmsnisansa/Classes/01...Sweeping algorithms manage 2 data sets ± Sweep-line status Gives the relationship among objects that the sweep line intersects; status

CS4522 Advanced Algorithmsnisansa/Classes/01...Sweeping algorithms manage 2 data sets ± Sweep-line status Gives the relationship among objects that the sweep line intersects; status

Documents

Chapter 3 Polygons. I. Properties of a Polygon A.A plane figure formed by three or more consecutive segments (sides or laterals) B. Each side intersects

Chapter 3 Polygons. I. Properties of a Polygon A.A plane figure formed by three or more consecutive segments (sides or laterals) B. Each side intersects

Documents

Polygons A Polygon is a closed plane figure formed by 3 or more segments Each segment intersects exactly 2 other segments only at their endpoints. No

Polygons A Polygon is a closed plane figure formed by 3 or more segments Each segment intersects exactly 2 other segments only at their endpoints. No

Documents