Regular Polygons Geometry Chapter 3 A BowerPoint Presentation.

Slides:

Advertisements

Similar presentations

The shapes below are examples of regular polygons

Advertisements

Objectives Classify polygons based on their sides and angles.

Polygons and Their Angles

Geometry 5 Level 1. Interior angles in a triangle.

Chapter 24 Polygons.

8.1 Angles of Polygons.

Chapter 6 Polygons. A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints. PolygonsNot Polygons.

Geometry Chapter Polygons. Convex Polygon – a polygon with a line containing a side with a point in the interior of the polygon.

Polygons – Sum of the Angles The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed.

Objectives Classify polygons based on their sides and angles.

GEOMETRY 10 TH GRADE GEOMETRY MS. FORTINO Regular Polygons Click to Proceed.

Aim 6.4: To explore the exterior angles of a polygon

Formulas involving Polygons

ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS. POLYGONS NOT POLYGONS.

6-1 The Polygon Angle-Sum Theorems

Chapter 6: Polygons and Quadrilaterals. Polygon terms we know: Kite Trapezoid Polygons Quadrilateral Rectangle Square Concave Convex Side Vertex Diagonal.

CHAPTER 24 Polygons. Polygon Names A POLYGON is a shape made up of only STRAIGHT LINES.

ANGLES OF POLYGONS SPI SPI Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals.

Objective: After studying this section, you will be able to recognize regular polygons and use a formula to find the measure of an exterior angle of an.

Lesson 8.2 (Part 2) Exterior Angles in Polygons

8.2 Angles in Polygons Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon.

CHAPTER 11 REVIEW. QUESTION ONE Find the sum of the interior angles of a convex decagon. A.1800° B. 1440° C. 360° D. 180°

Geometry Section 8.1 Find Angle Measures in Polygons.

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 2.5 Convex Polygons.

Warm Up 7.3 Formulas involving Polygons Use important formulas that apply to polygons.

Section 3.5 Polygons A polygon is:  A closed plane figure made up of several line segments they are joined together.  The sides to not cross each other.

Polygons What are properties (rules) of the different types of Quadrilaterals?

Lesson 10-4: Tessellation

Polygons and Area (Chapter 10). Polygons (10.1) polygon = a closed figure convex polygon = a polygon such that no line containing a side goes through.

Polygons – Angles In Regular Polygons Regular Polygons have equal sides and equal angles, So if we can find one side, we would know the measure of all.

Geometry. 3 sides 4 sides 5 sides 6 sides 8 sides 9 sides 10 sides 12 sides triangle quadrilateral pentagon hexagon octagon nonagon decagon dodecagon.

Area of Regular Polygons January 27, Objectives Learn the formula for the area of regular polygons.

Chapter 11-Area of Polygons & Circles Angle Measures in Polygons Section 11.1 Goal – To find the measures of interior and exterior angles of polygons.

1 Objectives Define polygon, concave / convex polygon, and regular polygon Find the sum of the measures of interior angles of a polygon Find the sum of.

Do Now. Section 8.2 Angles in Polygons Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex polygon with n sides.

Lesson 5.2 Polygon Exterior Angle Sum HOMEWORK: 5.2/ 1-10.

ANGLES OF POLYGONS. Polygons  Definition: A polygon is a closed plane figure with 3 or more sides. (show examples)  Diagonal  Segment that connects.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.

Holt McDougal Geometry 6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Holt Geometry Warm Up Warm Up Lesson Presentation.

The Interior Angles of Polygons. Sum of the interior angles in a polygon We’ve seen that a quadrilateral can be divided into two triangles … … and a pentagon.

2.5 How Can See It? Pg. 20 Classify Polygons. 2.5 – How Can I See It?______________ Classify Polygons In this section you will discover the names of the.

Holt Geometry 6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Holt Geometry Warm Up Warm Up Lesson Presentation Lesson.

Angle Measures in Polygons Chapter 11, Section 1 June 23, 2016.

Polygons 1 What is the difference between concave and convex?

LESSON 7.1 OBJ: The learner will use interior and exterior angles in a polygon. Do Now: Name the polygons with the given number of sides: 3, 4, 5, 6, 7,

# of sides # of triangles Sum of measures of interior angles 31 1(180)= (180)= (180)= (180)=720 n n-2(n-2) 180.

Polygons. Polygon Interior Angle Theorem The sum of the measures of the interior angles of a convex polygon is given by: Sum = 180(n – 2) where n represents.

POLYGONS 10/17/2007 NAMING POLYGONS

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

Determine the name of the polygon

6.1 The Polygon Angle-Sum Theorem

Problem of the Day Solve for y, justify your answer 15x (x + 7)

6-1 Angles of Polygons The student will be able to:

Interior angles in a triangle

Now let’s explore the sum of the 4 angles in any quadrilateral.

Polygons – Measurements of Angles

11.1 Angles Measures in a Polygon

Angles of a Polygon Diagonal of a polygon – A segment that connects any two nonconsecutive vertices. The number of triangles formed by drawing diagonals.

Angles in Polygons.

3-5 Angles of a Polygon.

An angle inside a polygon

ANGLES OF POLYGONS.

Polygons – Angles In Regular Polygons

How many diagonals in a… 1. Triangle _______ 2. Heptagon _______

Lesson 10-4: Tessellation

Angle Measures of Polygons

ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS.

Module 15: Lesson 1 Interior & Exterior Angles

Angle Measures in Polygons

Presentation transcript:

Regular Polygons Geometry Chapter 3 A BowerPoint Presentation

Regular polygon A regular polygon is – Equilateral (all sides are ) AND – Equilangular (all angles are )

Regular polygon A regular polygon is – Equilateral (all sides are ) AND – Equilangular (all angles are ) A regular triangle

Regular polygon A regular polygon is – Equilateral (all sides are ) AND – Equilangular (all angles are ) A regular quadrilateral (also known as a square) A regular quadrilateral (also known as a square)

Regular polygon A regular polygon is – Equilateral (all sides are ) AND – Equilangular (all angles are ) A regular hexagon

Interior angles of regular polygons What is the measure of each interior angle of this regular hexagon? There are six congruent sides & six congruent angles There are six congruent sides & six congruent angles

Interior angles of regular polygons What is the measure of each interior angle of this regular hexagon? Do you remember (n – 2) 180 ? [n is the # of sides] Do you remember (n – 2) 180 ? [n is the # of sides]

Interior angles of regular polygons What is the measure of each interior angle of this regular hexagon? (6 – 2) 180 = (4) 180 = 720° is the sum for int ∡s (6 – 2) 180 = (4) 180 = 720° is the sum for int ∡s

Interior angles of regular polygons What is the measure of each interior angle of this regular hexagon? 120° All interior ∡s are equal, so 720° / 6 = 120° All interior ∡s are equal, so 720° / 6 = 120°

Exterior angles of regular polygons What is the measure of each exterior angle of this regular hexagon? Do you remember what the sum of the exterior ∡ s of ANY convex polygon must = ?

Exterior angles of regular polygons What is the measure of each exterior angle of this regular hexagon? The sum of the exterior ∡ s of ANY convex polygon must = 360° !

Exterior angles of regular polygons What is the measure of each exterior angle of this regular hexagon? 60° All the exterior ∡ s are equal, so 360° / 6 = 60° ! All the exterior ∡ s are equal, so 360° / 6 = 60° !

Interior ∡ + Exterior ∡ = 180° Notice that at each vertex, the interior ∡ + the exterior ∡ = 180°

Interior ∡ + Exterior ∡ = 180° Notice that at each vertex, the interior ∡ + the exterior ∡ = 180° For regular polygons… if you know either the interior ∡ or the exterior ∡, it is easy to find the other one! (How?)

A BowerPowerful TIP When you are working on regular polygon problems, your BEST FRIEND is the…

A BowerPowerful TIP When you are working on regular polygon problems, your BEST FRIEND is the… EXTERIOR ∡

A BowerPowerful TIP When you are working on regular polygon problems, your BEST FRIEND is the… EXTERIOR ∡ 1) We know all the exterior angles of a regular polygon are equal

A BowerPowerful TIP When you are working on regular polygon problems, your BEST FRIEND is the… EXTERIOR ∡ 1)We know all the exterior angles of a regular polygon are equal, and 2)We know all the exterior angles of a regular polygon have a sum of 360°

Example #1- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 10°. How many sides does this regular polygon have? What is the measure of each interior ∡ ?

Example #1- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 10°. How many sides does this regular polygon have? What is the measure of each interior ∡ ? We are in great shape, because we know each exterior ∡ = 10° !

Example #1- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 10°. How many sides does this regular polygon have? Let’s start with the # of sides (which is the same as the # of angles) 360° / 10 = 36 sides

Example #1- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 10°. What is the measure of each interior ∡ ? We know exterior ∡ + interior ∡ = 180° 10° + interior ∡ = 180° each interior ∡ = 170°

YOU TRY- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 20°. How many sides does this regular polygon have? What is the measure of each interior ∡ ?

YOU TRY- You know the exterior ∡ Each exterior angle of a certain regular polygon has a measure of 20°. How many sides does this regular polygon have?18 sides What is the measure of each interior ∡ ? 160°

Example #2- You DON’T know the exterior ∡ Each interior angle of a certain regular polygon has a measure of 179°. How many sides does this regular polygon have? What is the measure of each exterior ∡ ?

Example #2- You DON’T know the exterior ∡ Each interior angle of a certain regular polygon has a measure of 179°. How many sides does this regular polygon have? What is the measure of each exterior ∡ ? Our best friend is the exterior ∡ - let’s find it first!

Example #2- You DON’T know the exterior ∡ Each interior angle of a certain regular polygon has a measure of 179°. What is the measure of each exterior ∡ ? exterior ∡ + interior ∡ = 180° exterior ∡ + 179° = 180° exterior ∡ = 1°

Example #2- You DON’T know the exterior ∡ Each interior angle of a certain regular polygon has a measure of 179°. How many sides does this regular polygon have? We can use exterior ∡ = 1° to help us find the number of sides.

Example #2- You DON’T know the exterior ∡ Each interior angle of a certain regular polygon has a measure of 179°. How many sides does this regular polygon have? Since each exterior ∡ = 1°, 360° / 1 = 360 sides

YOU TRY- You DON’T know the exterior ∡ A certain regular polygon has 10 sides. What is the measure of each interior ∡ ? What is the measure of each exterior ∡ ? [Remember which ∡ is your best friend!!!]

YOU TRY- You DON’T know the exterior ∡ A certain regular polygon has 10 sides. What is the measure of each interior ∡ ? 144° What is the measure of each exterior ∡ ? 36° [Did you find the exterior ∡ first?]

BowerPower.net