5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°

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5.1 Polygon Sum Conjecture

Transcript of 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°

Page 1: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°

5.1 Polygon Sum Conjecture

Page 2: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°

Angle Exploration

EquilateralTriangle60°

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Angle Exploration

Square90°

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Angle Exploration

RegularPentagon108°

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Angle Exploration

RegularHexagon120°

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Angle Exploration

RegularHeptagon129°

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Angle Exploration

RegularOctagon135°

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Angle Exploration

RegularNonagon140°

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Angle Exploration

RegularDecagon144°

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Angle Exploration

RegularDodecagon147°

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Angle Exploration• Summarize our

results

Sides Degrees3 60°4 90°5 108°6 120°7 129°8 135°9 140°

10 144°11 147°

Is there a correlation between the number of sides and the degrees?

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• What is the sum of the angles in each of the polygons

Angle Exploration

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Angle Exploration

• Summarize our results

Sides Total Degrees3 180° 60°4 360° 90°5 540° 108°6 720° 120°7 900° 129°8 1080° 135°9 1260° 140°

10 1440° 144°11 1620° 147°

Total Degrees in each polygon.

Do you see a pattern?

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Interior Angles in a Polygon

• The sum of the angles of the interior angles of a convex n-gon is (n-2)•180°

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Interior Angles in a Polygon

• What are the angle measures if the polygon is regular

• (n-2)•180°/n

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Sample Problems

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X=96

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X=85

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X=97

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X=117

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Exercise 12


WARM UP: 0 You know the meaning of equilateral. What do you think an equiangular polygon is? 0.

WARM UP: 0 You know the meaning of equilateral. What do you think an equiangular polygon is? 0.

WARM UP!!! polygon not a polygon A polygon is a plane figure. A polygon is a closed region. A polygon is formed by three or more line segments as its.

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What is a tessellation?Rotation Tessellation For rotation tessellations, the adjacent sides of the polygon must be congruent. Squares, equilateral triangles, regular hexagons, and

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3 UNDERSTANDING QUADRILATERALS - Testlabz · Ans. (a) The minimum interior angle possible for regular polygon is 60°. Because an equilateral triangle being a regular polygon of 3

3 UNDERSTANDING QUADRILATERALS - Testlabz · Ans. (a) The minimum interior angle possible for regular polygon is 60°. Because an equilateral triangle being a regular polygon of 3

Properties of Polygons UNIT 5 Teacher: Per: · 2020. 11. 29. · Polygon Sum Conjecture The sum of the measures of the n interior angles of an n-gon is… Exterior Angle Sum Conjecture

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Polygon Clipping - cse.iitd.ernet.inpkalra/csl781/polygon-clipping-filling.pdf · Clipping Polygon : Area primitive Polygon Clipping Simple Polygon: Planar set of ordered points No

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washburn.mpls.k12.mn.us · 2019. 2. 27. · Notes Lesson 5.1 - Polygon Sum Conjecture — page 256 Angles of a Quadrilateral 36 D Cø¶rve.ny c.30 348 A regular quadrilateral h' -ft.Æ

washburn.mpls.k12.mn.us · 2019. 2. 27. · Notes Lesson 5.1 - Polygon Sum Conjecture — page 256 Angles of a Quadrilateral 36 D Cø¶rve.ny c.30 348 A regular quadrilateral h' -ft.Æ

Chapter 14 by Julia Duffy and Evan Ribaudo. Vocabulary: Regular polygon- convex polygon that is both equilateral and equiangular Reminder: convex.

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Geometry 11.4 Areas of Regular Polygons. Definitions Regular polygon- a polygon that is equiangular and equilateral. In the upper right side of your paper,

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Polygon Properties - Ch 5 Quadrilateral Sum Conjecture The sum of the measures of the four angles of any quadrilateral is…....360 degrees. C-30 p. 256.

Polygon Properties - Ch 5 Quadrilateral Sum Conjecture The sum of the measures of the four angles of any quadrilateral is…....360 degrees. C-30 p. 256.

10.4 Areas of Regular Polygons Geometry. Objectives/Assignment Find the area of an equilateral triangle. Find the area of a regular polygon, such as the.

10.4 Areas of Regular Polygons Geometry. Objectives/Assignment Find the area of an equilateral triangle. Find the area of a regular polygon, such as the.

Given a regular polygon, you can find its area by dividing the polygon into congruent, non- overlapping, equilateral triangles.

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Polygon Potpourri - dy/dan · the interior angles of a concave polygon? Conjecture: Proof: Investigation #2.!What is the sum of the measures of the exterior angles of a concave polygon?!

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Analytic Geometry Study Guide 2014.2015 (2) - PC\|MACimages.pcmac.org/.../Analytic_Geometry_Study_Guide_2014.pdf · Analytic Geometry Study Guide Equilateral: The property of a polygon

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Shape, Space and Measures Policy · trapezium and kite. Name equilateral triangle and isosceles triangles and heptagons, and know the term polygon and that polygons can be regular

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