(8) Lesson 5.4 - Polygons and Angles
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1. The document provides examples of using algebraic concepts to solve geometric problems about angles of triangles and polygons. 2. It introduces the formula for finding the sum of interior angles of any polygon: the sum is (n-2)180, where n is the number of sides. 3. Several examples demonstrate using this formula and setting up equations to calculate missing angle measures in triangles and regular polygons with a known number of sides.
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1. The document discusses classifying pairs of angles as complementary, supplementary, or neither. It also discusses finding the measure of an unknown angle using the fact that angles in a triangle sum to 180 degrees.
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1. The document provides examples and explanations of different types of angle relationships including: complementary angles, supplementary angles, adjacent angles, linear pairs, and vertical angles. Examples are worked through step-by-step to find the measures of unknown angles using properties of these relationships.
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Some slides lifted from: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CEsQFjAD&url=http%3A%2F%2Fdionmath.wikispaces.com%2Ffile%2Fview%2F2.3%2BComplementary%2Band%2BSuppl.%2BAngles.ppt&ei=_wVFUbzHCa-o4AP9ooGwBQ&usg=AFQjCNF-KDyDx_yiVaUuMJMdM6yOJqHASQ&sig2=wH2TZ9xGxsHgtc4cCnn2QQ&bvm=bv.43828540,d.dmg&cad=rja
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(8) Lesson 7.5 - Similar Triangles and Indirect measurement
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2. Key theorems discussed include the sum of interior angles of any polygon being 180(n-2) degrees and the sum of exterior angles of any polygon being 360 degrees.
3. Examples are provided to demonstrate calculating sums of interior and exterior angles using the theorems, determining the number of sides of a polygon given angle sums, and finding measures of individual angles.
Interior-and-Exterior-Angles-of-Polygons.ppt
The document discusses interior and exterior angles of polygons. It states that the sum of the interior angles of a convex polygon with n sides is (n-2)180 degrees. It also states that the sum of the exterior angles of any convex polygon is 360 degrees. Some examples are provided to demonstrate calculating interior and exterior angles of different polygons.
Geometry Section 4-1
This document defines key vocabulary terms related to triangles, including different types of triangles based on angle measures. It presents the Triangle Angle-Sum Theorem and Exterior Angle Theorem, along with their corollaries. It includes three multi-step examples solving for angle measures using these theorems and properties of triangles. The document provides definitions, theorems, examples and step-by-step workings to explain angles of triangles.
8 2 Triangle Sum Theorem
The document discusses several geometry theorems including:
1. The Triangle Sum Theorem which states that the sum of the interior angles of any triangle is 180 degrees.
2. The theorem that the sum of the interior angles of any quadrilateral is 360 degrees.
3. The Exterior Angle Theorem which states that an exterior angle of a triangle is equal to the sum of the two remote interior angles.
The document provides examples of using these theorems to prove other statements and find missing angle measures in geometric figures. It also assigns practice problems for students.
Properties of triangles
1) The document discusses geometry concepts related to angles of triangles including the triangle angle sum theorem, exterior angle theorem, and finding measures of unknown angles using known information.
2) Key details include that the sum of the interior angles of any triangle is 180 degrees, and the measure of an exterior angle is equal to the sum of the remote interior angles.
3) Examples are provided to demonstrate using these theorems to find the measures of missing angles in different triangle scenarios.
Hprec8 2
1) The document discusses inverse trigonometric functions such as arcsin, arccos, and arctan. It reviews special angle identities and defines the inverse trig functions.
2) Examples are provided to demonstrate evaluating inverse trig functions and writing equations in inverse form. The principal values of inverse trig functions are defined as being between -90 and 90 degrees.
3) The document contains examples of using inverse trig functions to find missing side lengths in 30-60-90 and 45-45-90 triangles based on special angle identities, as well as evaluating expressions involving inverse trig functions.
MATHEMATICS 7-SUM OF THE INTERIOR ANGLES
The document provides learning objectives and examples for understanding interior angles of polygons:
- It defines key terms like polygon, vertex, diagonal, and angle.
- It shows that the sum of interior angles of a triangle is 180 degrees and derives a formula to find the sum for any polygon: the sum equals (n-2) x 180 degrees, where n is the number of sides.
- Examples demonstrate using the formula to find sums and measure individual angles for different regular polygons.
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Lesson 1.6 (8)
Here are the steps to write a number between 0 and 1 in scientific notation with an example:
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2. Count the number of decimal places in the number. In this example there are 4 decimal places.
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(8) Lesson 5.4 - Polygons and Angles
- 1. Course3, Lesson 5-4 Find the value of x in each triangle. 1. 2. 3. Two angles of a triangle measure 35° and 65°. What is the measure of the third angle? 4. Two angles of a triangle measure 25° and 45°. What is the measure of the third angle? 5. The measures of the angles of a triangle are in the ratio 2:3:3. What are the measures of the angles?
- 2. Course3, Lesson 5-4 ANSWERS 1. 90 2. 15 3. 100° 4. 110° 5. 45°; 67.5°; 67.5°
- 3. HOW can algebraic concepts be applied to geometry? Geometry Course3, Lesson 5-4
- 4. Course3, Lesson 5-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Geometry • Extension of 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by transversal, and the angle-angle criterion for similarity of triangles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics.
- 5. To • find the measure of an interior or exterior angle of a regular polygon Course3, Lesson 5-4. Geometry
- 6. • polygon • equiangular • regular polygon Course3, Lesson 5-4 Geometry
- 7. Course3, Lesson 5-4 Geometry Words The sum of the measures of the interior angles of a polygon is (n – 2)180, where n represents the number of sides. Symbols S = (n – 2)180
- 8. 1 Need Another Example? 2 3 4 Step-by-Step Example 1. Find the sum of the measures of the interior angles of a decagon. The sum of the measures of the interior angles of a decagon is 1,440°. S = (8)180 or 1,440 Write the equation.S = (n – 2) 180 A decagon has 10 sides. Replace n with 10. Simplify. S = (10 – 2) 180
- 9. Answer Need Another Example? Find the sum of the measures of the interior angles of a 13-gon. 1,980°
- 10. 1 Need Another Example? 2 3 Step-by-Step Example 2. Each chamber of a bee honeycomb is a regular hexagon. Find the measure of an interior angle of a regular hexagon. Find the sum of the measures of the angles. Write an equation.S = (n – 2) 180 Simplify. The sum of the measures of the interior angles is 720°. Replace n with 6.S = (6 – 2) 180 S = (4)180 or 720 Divide 720 by 6, the number of interior angles, to find the measure of one interior angle. So, the measure of one interior angle of a regular hexagon is 720° ÷ 6 or 120°.
- 11. Answer Need Another Example? A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon. 108°
- 12. Course3, Lesson 5-4 Geometry Words In a polygon, the sum of the measures of the exterior angles, one at each vertex, is 360˚ Model Symbols 1 2 3 4 5 360m m m m m
- 13. 1 Need Another Example? 2 3 Step-by-Step Example 3. Find the measure of an exterior angle in a regular hexagon. Let x represent the measure of each exterior angle. Write an equation. A hexagon has 6 exterior angles.6x = 360 Division Property of Equalityx = 60 So, each exterior angle of a regular hexagon measures 60°.4
- 14. Answer Need Another Example? Find the measure of an exterior angle in a regular 30-gon. 12°
- 15. How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-4 Geometry
- 16. How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-4 Geometry Sample answers: • You use a formula to find the sum of the interior angles of any polygon. • You can write an equation to find the measure of a missing interior or exterior angle of a polygon.
- 17. Explain how to find the sum of the interior angles of a polygon when you know the number of sides of the polygon. Ratios and Proportional RelationshipsFunctionsGeometry Course 3, Lesson 5-4