The Polygon Angle-Sum Theorems

Slides:



Advertisements
Similar presentations
The Polygon Angle-Sum Theorems
Advertisements

Quadrilaterals and Other Polygons
Objectives Classify polygons based on their sides and angles.
Accelerated Algebra/Geometry Mrs. Crespo
Polygons and Their Angles
Geometry 6.1 Prop. & Attributes of Polygons
6.1: Properties of Polygons
6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation
Properties and Attributes of Polygons
6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation
3.4 Polygons (2 cards). Polygons Naming Polygons  Name the Polygon  Name the Vertices  Name the Sides  Name the Angles.
3.5 The Triangle Sum Theorem
3.6 Angles in Polygons Objectives: Warm-Up:
WARM-UP Tuesday, February 24, 2015
3.4: The Polygon Angle-Sum Theorem
1. Find the measure of the supplement of a 92° angle. 2. Evaluate (n – 2)180 if n = Solve = 60.
NAMING POLYGONS.
Objectives Classify polygons based on their sides and angles.
6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation
6-1 Properties and Attributes of Polygons Holt McDougal Geometry
Angles of Polygons.
3-5 The Polygon Angle-Sum Theorems
Polygons & Quadrilaterals
Chapter properties of polygons. Objectives  Classify polygons based on their sides and angles.  Find and use the measures of interior and exterior.
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.
Section 3-4 Polygon Angle-Sum Theorem SPI 32A: Identify properties of plane figures from information given in a diagram Objectives: Classify Polygons Find.
Objectives Classify polygons based on their sides and angles.
5.7 Angle Measures in Polygons. Vocabulary/Theorems  Diagonal: joins 2 nonconsecutive vertices  Convex Polygon: has no vertex going into the interior.
Simplify the expression 6y-(2y-1)-4(3y+2) a. -8y-7b. -8y-3 c. -8y+1d. -8y warm-up 2.
Name the polygons with the following number of sides:
Chapter 3 Lesson 4 Objective: Objective: To classify polygons.
The Polygon Angle- Sum Theorems
11-1 Angle Measures in Polygons Warm Up Lesson Presentation
8.2 Angles in Polygons Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon.
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.
Is it too much to ask for a LITTLE PRECIPITATION?! -Evan Lesson 4: (3.5) The Polygon Angle-Sum Theorems LT: To classify polygons and to find the measures.
 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.
+ Polygon Angle Sum Theorem (3.4) Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons.
Angles of Polygons Find the sum of the measures of the interior angles of a polygon Find the sum of the measures of the exterior angles of a This scallop.
Drill 1)If two angles of a triangle have a sum of 85 degrees find the third angle. 2) The three angles of a triangle are 2x, 3x, and 2x + 40 find each.
Convex vs. Concave Polygons Interior Angles of Polygons Exterior Angles of Polygons Polygons.
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.
GEOMETRY HELP Name the polygon. Then identify its vertices, sides, and angles. The polygon can be named clockwise or counterclockwise, starting at any.
Date: 8.1(a) Notes: Polygon Interior Angles Sum Lesson Objective: Find and use the sum of the measures of the interior angles of a polygon. CCSS: G.MG.1.
$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.
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.
Section 6-1 Properties of Polygons. Classifying Polygons Polygon: Closed plane figure with at least three sides that are segments intersecting only at.
POLYGONS. Examples of Polygons: NOT Examples of Polygons: Definition of a Polygon A polygon is a closed figure formed by a finite number of coplanar segments.
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.
8.1 Find Angle Measures in Polygons Hubarth Geometry.
Journal 6: Polygons Delia Coloma 9-5.
The Polygon Angle-Sum Theorem. Check Skills You’ll Need Find the measure of each angle of quadrilateral ABCD
Objectives Classify polygons based on their sides and angles.
Determine the name of the polygon
Sum of Interior and Exterior Angles in Polygons
6-1 Angles of Polygons The student will be able to:
Vocabulary side of a polygon vertex of a polygon diagonal
6-1 Properties and Attributes of Polygons Lesson Presentation
6.1 Notes: Angles of Polygons
Lesson 3-4 Polygons Lesson 3-4: Polygons.
Objectives Classify polygons based on their sides and angles.
3.4 The Polygon Angle-Sum Theorems
The Polygon Angle-Sum Theorems
The Polygon Angle-Sum Theorems
Vocabulary side of a polygon vertex of a polygon diagonal
HW: P even, 29, and 30..
Lesson 3-4 Polygons.
The Polygon Angle-Sum Theorem
Lesson 3-4 Polygons.
Presentation transcript:

The Polygon Angle-Sum Theorems Lesson 3-5 Additional Examples Name the polygon. Then identify its vertices, sides, and angles. Its sides are AB or BA, BC or CB, CD or DC, DE or ED, and EA or AE. Its vertices are A, B, C, D, and E. Its angles are named by the vertices, A (or EAB or BAE), B (or ABC or CBA), C (or BCD or DCB), D (or CDE or EDC), and E (or DEA or AED). The polygon can be named clockwise or counterclockwise, starting at any vertex. Possible names are ABCDE and EDCBA.

The Polygon Angle-Sum Theorems Lesson 3-5 Additional Examples Classify the polygon below by its sides. Identify it as convex or concave. Starting with any side, count the number of sides clockwise around the figure. Because the polygon has 12 sides, it is a dodecagon. Think of the polygon as a star. If you draw a diagonal connecting two points of the star that are next to each other, that diagonal lies outside the polygon, so the dodecagon is concave.

The Polygon Angle-Sum Theorems Lesson 3-5 Additional Examples Find the sum of the measures of the angles of a decagon. A decagon has 10 sides, so n = 10. Sum = (n – 2)(180) Polygon Angle-Sum Theorem = (10 – 2)(180) Substitute 10 for n. = 8 • 180 Simplify. = 1440

The Polygon Angle-Sum Theorems Lesson 3-5 Additional Examples Find m X in quadrilateral XYZW. The figure has 4 sides, so n = 4. m X + m Y + m Z + m W = (4 – 2)(180) Polygon Angle-Sum Theorem m X + m Y + 90 + 100 = 360 Substitute. m X + m Y + 190 = 360 Simplify. m X + m Y = 170 Subtract 190 from each side. m X + m X = 170 Substitute m X for m Y. 2m X = 170 Simplify. m X = 85 Divide each side by 2.

The Polygon Angle-Sum Theorems Lesson 3-5 Additional Examples A regular hexagon is inscribed in a rectangle. Explain how you know that all the angles labeled 1 have equal measures. Sample: The hexagon is regular, so all its angles are congruent. An exterior angle is the supplement of a polygon’s angle because they are adjacent angles that form a straight angle. Because supplements of congruent angles are congruent, all the angles marked 1 have equal measures.