Geometry 6.1 Polygons.

Slides:

Advertisements

Similar presentations

Objectives Classify polygons based on their sides and angles.

Advertisements

Geometry 6.1 Prop. & Attributes of Polygons

3.4 The Polygon Angle-Sum Theorems

3.4: The Polygon Angle-Sum Theorem

Angles of Polygons.

Objectives Classify polygons based on their sides and angles.

Angles of Polygons.

3.4: THE POLYGON ANGLE-SUM THEOREM OBJECTIVE: STUDENTS WILL BE ABLE TO… TO CLASSIFY POLYGONS, AND TO FIND THE SUMS OF INTERIOR AND EXTERIOR ANGLES OF POLYGONS.

Name the polygons with the following number of sides:

The Polygon Angle- Sum Theorems

Friday, Feb. 22, 2013 Agenda: TISK & No MM HW Check Lesson 10-1: Polygons Homework: 10-1 problems in packet A B C

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

6.1 Polygons 6.2 Properties of Parallelograms Essential Question: How would you describe a polygon?

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 the.

Section 3-5 Angles of a Polygon. many two endpoint collinear Yes No angles.

Section 3-5: The Polygon Angle-Sum Theorem. Objectives To classify polygons. To find the sums of the measures of the interior and exterior angles of a.

Polygon – Shape with many angles; each segment (side) must intersect exactly 2 other segments.

Warm-Up Draw an example of a(n)…

Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying.

 A Polygon is a closed plane figure with at least three sides. The sides intersect only at their endpoints, and no adjacent sides are collinear. A. B.

Name the polygons with the following number of sides: Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon.

+ Polygon Angle Sum Theorem (3.4) Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons.

Polygons Geometry.

Chapter 1.6 Notes: Classify 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.

Chapter 6 Quadrilaterals Sec 6.1 Polygons. Polygon 1.Is a plane figure that is formed by 3 or more segments. No two sides with common endpoint are collinear.

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

3-5 Angles of a Polygon. A) Terms Polygons – each segment intersects exactly two other segments, one at each endpoint. Are the following figures a polygon?

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.

Quadrilaterals Sec 6.1 GOALS: To identify, name, & describe quadrilaterals To find missing measures in quadrilaterals.

Polygon Angle-Sum. A polygon is a closed plane figure with at least three sides. The sides intersect only at their endpoints and no adjacent sides are.

Polygon Closed plane figure with at least three sides The sides intersect only at their endpoints No adjacent sides are collinear To name a polygon –Start.

Section 6-1 Polygons. Polygon Formed by three or more segments called sides. No two sides with a common endpoint are collinear. Each side intersects exactly.

3-4: The polygon Angle-Sum Theorems

Chapter 6: Quadrilaterals Section 6.1: Polygons. polygon – a plane figure that meets the following conditions. 1)It is formed by three or more segments.

Other polygons November 12, Objectives Content Objectives Learn about properties of polygons, beyond triangles and quadrilaterals. Language Objectives.

POLYGONS 10/17/2007 NAMING POLYGONS

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

Objectives Classify polygons based on their sides and angles.

Chapter 6 Section 6.1 Polygons.

Lesson 3-5 Polygons.

10.1 Polygons Geometry.

Sum of Interior and Exterior Angles in Polygons

Section 3-5 Angles of a Polygon.

Section Classify Polygons Objective: SWBAT classify polygons

Chapter 8: Quadrialterals

3-5 Angles of a Polygon.

Lesson 7.1 Angles of Polygons.

Angles of Polygons.

6.1 Vocabulary Side of a polygon Vertex of a polygon Diagonal

Classifying Polygons Section 8.1.

Lesson 3-4 Polygons Lesson 3-4: Polygons.

3.4 The Polygon Angle-Sum Theorems

Chapter 6 Section 6.1 Polygons.

The Polygon Angle-Sum Theorems

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

6.1 Polygons Geometry.

Chapter 1 – Essentials of Geometry

Lesson 3-4 Polygons.

Section 2.5 Convex Polygons

Polygons and Angles Sec 12 -1E pg

Section 6.1 Polygons.

Lesson 3-4 Polygons.

Presentation transcript:

Geometry 6.1 Polygons

Goals: Identify polygons & describe them. Determine the measure of angles in a quadrilateral. November 9, 2018 Geometry 6.1 Polygons

Polygon A plane figure made of three or more segments (sides). Each side intersects exactly two other sides at their endpoints. Polygons are named by vertices in consecutive order, going CW. November 9, 2018 Geometry 6.1 Polygons

Examples November 9, 2018 Geometry 6.1 Polygons

Sides don’t intersect at endpoints. These are NOT polygons. Figure not closed. No Sides or Segments Sides don’t intersect at endpoints. November 9, 2018 Geometry 6.1 Polygons

Naming Polygons The name tells you how many sides and how many vertices the polygon has. Learn the names: memorize! Be able to spell them. November 9, 2018 Geometry 6.1 Polygons

Triangle – 3 sides C Name: ABC A B November 9, 2018 Geometry 6.1 Polygons

Quadrilateral – 4 sides Q T R S Name: QRST November 9, 2018 Geometry 6.1 Polygons

Pentagon – 5 sides N Name: JKLMN M J K L November 9, 2018 Geometry 6.1 Polygons

Hexagon – 6 sides C B A D E F Name: FEDCBA November 9, 2018 Geometry 6.1 Polygons

Heptagon – 7 sides November 9, 2018 Geometry 6.1 Polygons

Octagon – 8 sides November 9, 2018 Geometry 6.1 Polygons

Nonagon – 9 sides November 9, 2018 Geometry 6.1 Polygons

Decagon – 10 sides November 9, 2018 Geometry 6.1 Polygons

More than 10 sides: n-gon 14-gon has 14 sides. 200-gon has 200 sides. November 9, 2018 Geometry 6.1 Polygons

Diagonals A segment that joins two non-consecutive vertices. November 9, 2018 Geometry 6.1 Polygons

Convex & Concave All polygons are either convex or concave. It’s easy to determine which category falls in just by looking. November 9, 2018 Geometry 6.1 Polygons

Convex All diagonals are in the interior of the polygon. November 9, 2018 Geometry 6.1 Polygons

Concave Think: Caved In At least one diagonal (or part of one) is in the exterior of the polygon. November 9, 2018 Geometry 6.1 Polygons

Equilateral Polygons All sides are congruent. November 9, 2018 Geometry 6.1 Polygons

Equiangular Polygons All the angles have the same measure. November 9, 2018 Geometry 6.1 Polygons

REGULAR Polygons Are equilateral AND equiangular. November 9, 2018 Geometry 6.1 Polygons

Theorem 6.1 The sum of the angles of a quadrilateral is 360. 4 1 2 3 1 + 2 + 3 + 4 = 360 November 9, 2018 Geometry 6.1 Polygons

Proof B + 1 + 3 = 180 D + 2 + 4 = 180 A B C D 3 4 1 2 B + 1 + 3 = 180 D + 2 + 4 = 180 B + D + (1 + 2) + (3 + 4) = 360 But 1 + 2 = A and 3 + 4 = C B + D + A + C = 360 November 9, 2018 Geometry 6.1 Polygons

Example Solve for x. x 55 55 x + x + 55 + 55 = 360 2x + 110 = 360 November 9, 2018 Geometry 6.1 Polygons

Your Turn Find the measure of each angle. A D B C (5x + 10) November 9, 2018 Geometry 6.1 Polygons

Solution 80 132 82 66 A D B C (5x + 10) (4x + 10) (3x + 40) (5x + 10) + (8x + 20) + (3x + 40) + (4x + 10) = 360 20x + 80 = 360 20x = 280 x = 14 November 9, 2018 Geometry 6.1 Polygons