Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

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Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3

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Transcript of Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Page 1: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Parallel Lines and the Triangle Angle-Sum Theorem

Geometry

Mrs. King

Unit 3, Lesson 3

Page 2: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Theorem 2-1Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180.

Page 3: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Video: Sum of the Angles of a Triangle

Page 4: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Find the measure of the missing angle

http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gifhttp://maths.fallibroome.cheshire.sch.uk/triangle.jpg

http://www.gizapyramid.com/basic_triangle_w-angles.gif

x

x

Page 5: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Practice

• Find all Variables:

Page 6: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Practice

• Find all Variables:

Page 7: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Practice

• Find all variables

Page 8: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Definition

Exterior Angle: an angle formed by the side of a polygon and an extension of a side.

http://www.freemathhelp.com/images/lessons/exterior1.gif

Page 9: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Definition

Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.

http://www.freemathhelp.com/images/lessons/exterior1.gif

Page 10: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Theorem 2-2Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Page 11: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Find the measure of the missing angle

http://www.kwiznet.com/px/homes/i/grade8/math/Grade_VIII_Triangles_And_Polygons_PB2_QuestionNo.5.gif

Page 12: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Find the measure of the missing angle

http://www.freemathhelp.com/images/lessons/exterior2.gif

Page 13: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Definition

Corollary: a statement that follows directly from a theorem.

Page 14: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Corollary to Theorem 2-2

The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.

Page 15: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Types of Triangles (by sides)

• Equilateral

• Isosceles

• Scalene

Page 16: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Equilateral Triangles

• Definition:– A triangle with three

congruent sides.

• Example:

Page 17: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Isosceles Triangles

• Definition:– A triangle with two

congruent sides.

• Example:

Page 18: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Scalene Triangles

• Definition:– A triangle with no

congruent sides.

• Example:

Page 19: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Types of Triangles (by angle)

• Equiangular

• Acute

• Right

• Obtuse

Page 20: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Equiangular Triangles

• Definition:– A triangle with three

congruent angles.

• Example:

Page 21: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Acute Triangles

• Definition:– A triangle whose

angles are all acute.

• Example:

Page 22: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Right Triangles

• Definition:– A triangle with one

right angle.

• Example:

Page 23: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

Obtuse Triangles

• Definition:– A triangle with one

obtuse angle.

• Example:

Page 24: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.

The three sides of the triangle have three different lengths, so the triangle is scalene.One angle has a measure greater than 90, so the triangle is obtuse.

The triangle is an obtuse scalene triangle.

Classify the triangle by its sides and its angles.


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