Unit 6: Geometry

Minds On

• Draw a triangle on a blank piece of paper

• Measure all interior angles• Measure all exterior angles• Make conclusions about the interior

and exterior angles of a triangle

Make a Triangle!

Unit 6: Geometry

Minds On

Conclusions

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon Angles

Learning Goals

I can describe the relationship between the exterior and interior angles of a triangle and use these relationships to find missing angle measurement

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon Angles

Review – Types of Triangles

Unit 6: GeometryLesson Two: Triangle and Other Polygon

AnglesVocabularyVertex – Where two line segments join or meet.

Polygon – a two-dimensional shape made of 3 or more lines that join together to make a closed loop.

Interior Angle – The angle formed inside a polygon by two sides meeting at a vertex.

Exterior Angle – The angle formed at the vertex by one side of a polygon that has been extended through the vertex, and an original side.

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon Angles

1. The interior angles of a triangle add up to 1802. The exterior angles of a triangle add up to 3603. The value of an exterior angle is equal to the

sum of the two interior angles at the opposite vertices.

We call them the Remote Interior Angles.

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon Angles

Example 1: Determine the value of :

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon Angles

Example 2: Determine the value of :

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon AnglesExample 3: Determine the value of :

Unit 6: Geometry

Lesson Two: Triangle and Other Polygon AnglesExample 4: Determine the value of :

Unit 6: Geometry

Learning Goals

I can determine the sum of interior and exterior angles of various regular polygons

I can use the properties of polygons to find unknown side lengths and missing angle measurements.

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

Vocabulary

Regular Polygon: a polygon that has equal side lengths and equal interior angles. (An equilateral triangle is an example)

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

General rule for polygon angles:

In polygon with n sides:• the sum of the interior angles is 180(n – 2)° • the sum of the exterior angles is 360°

WHY??

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

Example 1: Determine the value of :

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

Example 2: Determine the value of and the value of each angle:

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

Example 3: Determine the value of the interior and exterior angles for this decagon.(Hint, this is a regular polygon)

Lesson Two: Triangle and Other Polygon Angles

Unit 6: Geometry

Practice

Pg. 365 #1bcd, 2cdefgh, 3, 4, 6abc, 8, 9b, 10b

Pg. 371 # 1, 2, 4, 7 Pg. 377 # 1, 2, 4

Lesson Two: Triangle and Other Polygon Angles