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

Theorem 2-1Triangle Angle-Sum Theorem

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

Video: Sum of the Angles of a Triangle

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

Practice

• Find all Variables:

Practice

• Find all Variables:

Practice

• Find all variables

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

Definition

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

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.

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

Definition

Corollary: a statement that follows directly from a theorem.

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.

Types of Triangles (by sides)

• Equilateral

• Isosceles

• Scalene

Equilateral Triangles

• Definition:– A triangle with three

congruent sides.

• Example:

Isosceles Triangles

• Definition:– A triangle with two

congruent sides.

• Example:

Scalene Triangles

• Definition:– A triangle with no

congruent sides.

• Example:

Types of Triangles (by angle)

• Equiangular

• Acute

• Right

• Obtuse

Equiangular Triangles

• Definition:– A triangle with three

congruent angles.

• Example:

Acute Triangles

• Definition:– A triangle whose

angles are all acute.

• Example:

Right Triangles

• Definition:– A triangle with one

right angle.

• Example:

Obtuse Triangles

• Definition:– A triangle with one

obtuse angle.

• Example:

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.

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

Documents

Properties of Parallel Lines...Feb 14, 2011 · 3‐3 Parallel and Perpendicular Lines 3‐4 Parallel Lines and the Triangle Angles‐Sum Theorem 3‐5 The Polygon Angle‐Sum Theorem

Triangle Sum Theorem & Exterior Angle Theorem. Work in groups to answer the questions. Try your best. 1.Name 2 pair of alternate interior angles 5 &

Math Tech 1 · 8-2 Finding the Missing Angle of a Triangle A TRIANGLE ANGLE SUM THEOREM: All three angles of a triangle will add up to equal 180

Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

3.1 & 3.2 -Triangle Sum Theorem & Isosceles Trianglesridavis.weebly.com/uploads/8/7/2/6/87260484/chapter_3___4_notes.pdfUnit 2 4.1 & 4.2 -Similar Triangle Theorems Standard G.SRT.2:

8.1 Pythagorean Theorem and Its Converse Pythagorean Theorem –If a triangle is a right triangle, then the sum of the squares of the lengths of the legs

Section 3.3 Triangles Thompson. Triangle Sum Theorem The sum of the measures --?--

Triangle Sum Theorem. Draw a Triangle Make sure your lines are dark!

Triangle AngleSum Theorem1 Jul 24 9:36 AM 3.4 Triangle Angle Theorems I CAN... Apply the Triangle Angle Sum Theorem and Exterior Angle Theorem Jul 24 9:36 AM Triangle Angle Sum Theorem

8 2 Triangle Sum Theorem

Burlington County Institute of Technology Curriculum Document · apply the Triangle Angle-Sum Theorem and Exterior Angle Theorem. name and use corresponding parts of congruent polygons

4-1 Triangles and Angles. Theorem 4.1: Triangle Sum The sum of the measures of the interior angles of a triangle is 180 . xx yy zz x +

What is the Pythagorean Theorem? The Pythagorean Theorem relates the side lengths of a right triangle. In any right triangle, the sum of the squares

Triangle Application Theorems Lesson 7.1. Theorem 50- The sum of the measures of the angles of a triangle is 180º

€¦ · Pythagorean Theorem Parts of a Right Triangle -legs -hypotenuse Pythagoream Theorem - 'm a right triangle, the sum of the squares of the legs is equal to the square of the

4.1 Apply Triangle Sum Properties. Objectives Identify and classify triangles by angles or sides Apply the Angle Sum Theorem Apply the Exterior

8 The Pythagorean Theorem - imater.org€¦ · Theorem 8-1 Pythagorean Theorem Theorem If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is

The Triangle Midsegment Theorem

TRIANGLE INEQUALITY THEOREM

Triangle Sum Theorem