ANGLES OF A TRIANGLE Section 4.2. Angles of a Triangle Interior angles  Original three angles of a triangle Exterior angles  Angles that are adjacent.

Slides:

Advertisements

Similar presentations

Draw the following: 1. acute triangle 2.right triangle 3.obtuse triangle 4. acute, scalene triangle 5.obtuse, isosceles triangle 6. right, scalene.

Advertisements

The Triangle Sum Theorem.  The sum of the measures of the angles of a triangle are equal to 180 degrees < 5 = < 3 and < 4= < 1 because alternate.

3.5 Parallel Lines and Triangles

Classifying Triangles

4.2 Angles of Triangles Objectives: *Apply the Angle Sum Theorem.

An exterior angle is outside the triangle and next to one of the sides. 4-2 Exterior Angle Theorem.

7.2 Exterior Angle Theorem. You will learn to identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem. 1)

3-5 Parallel Lines and Triangles

ANGLES OF TRIANGLES HEXAHEDRON: This is your standard cube, but "Hex" comes from the Greek meaning "six." About the only fascinating thing about this.

4-2 Angles of Triangles Objectives: The student will be able to: 1. Apply the Triangle-Sum Theorem. 2. Apply the Exterior Angle Theorem.

HOW TO FIND AN ANGLE MEASURE FOR A TRIANGLE WITH AN EXTENDED SIDE

Triangles 1 The Basics. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB∆CBA∆BCA.

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

Chapter 4 Congruent Triangles. 4.1 & 4.6 Triangles and Angles Triangle: a figure formed by three segments joining three noncollinear points. Classification.

Classifying Triangles

Classifying Triangles Angle Measures of Triangles.

5-6 Inequalities in One Triangle

Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180°

Angles of Triangles Chapter 4, Section 2. Angle Sum Theorem The sum of angles in a triangle is 180 o

Types of Triangles And Angle Sum Theorems.  Notation for sides.  AB CB AC  Angles   ABC or  B  Vertex angle  Base angle  Opposite side  Opposite.

Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem.

Classify triangles by sides No congruent sides Scalene triangle At least two sides congruent Isosceles triangle Three congruent sides Equilateral triangle.

Goal, to classify triangles by their sides and by their angles.

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

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

Chapter 4 Section 4.1 Section 4.2 Section 4.3. Section 4.1 Angle Sum Conjecture The sum of the interior angles of a triangle add to 180.

I can use theorems, postulates and/or definitions to prove theorems about triangles including: measures of interior angles of a triangle sum to 180 degrees.

Geometry Triangles. Vocabulary  Theorem 4-1 (angle sum theorem): The sum of the measures of the angles of a triangle is 180 In order to prove the angle.

 4.1 Classifying Triangles. Example 1 Example 2.

Angles of Triangles Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 degrees. Third Angle Theorem If two angles of one triangle.

Sec: 3.5 Sol: G.2c  Interior angles  Exterior angles.

Angles Outside the Triangle 4-1B What are remote interior angles? What is the relationship between an exterior angle and the remote interior angles?

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

+ Angle Relationships in Triangles Geometry Farris 2015.

3-4 Angles of a Triangle. A Triangle is a figure formed by three segments joining three noncollinear points. 1) Classifying triangles by their sides.

Geometry Section 4.1 Apply Triangle Sum Properties.

CH. 4.1 APPLY TRIANGLE SUM PROPERTIES. VOCAB Interior Angles : angles inside the triangle (sum = 180) Exterior Angles: angles outside the triangle Interior.

Exterior Angles.

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Angles of Triangles.

Week 3 Warm Up State the number of sides: 1) Trapezoid

Measuring Angles in Triangles

Section 4-1 Triangles and Angles.

Chapter 4: Congruent Triangles

WARM UP What is the sum of the angle measures of each triangle?

Angle Theorems for Triangles

Geometry 4.1 Triangle and Angles.

Angles of Triangles 4.2.

Exterior Angles of Triangles

Section 3-4 Angles of a Triangle.

Types of Triangles and Their Properties

5.5 Inequalities in One Triangle

Triangle Application Theorems

6.5 & 6.6 Inequalities in One and Two Triangle

Warm-up Find x a) b).

Objectives -triangle names -remote interior -exterior

Exterior Angles of Triangles

V L T The sum of the interior angles of a triangle is 180 degrees.

Triangle Theorems.

Lesson 18 Triangle Theorems.

Base Angles & Exterior Angles

Drill 1) x = 180, solve for x 2) How many degrees do the interior angles of a triangle add up to. 3) What type of triangle has an angle that.

Exterior Angle Theorem

3-3 Parallel Lines & the Triangle Angle Sum Theorem

Classifying Triangles

5.2-Inequalities and Triangles

Geometry 3.4 Angles of a Triangle.

Bellwork Solve for the variable.

Module 15: Lesson 1 Interior & Exterior Angles

Presentation transcript:

ANGLES OF A TRIANGLE Section 4.2

Angles of a Triangle Interior angles  Original three angles of a triangle Exterior angles  Angles that are adjacent to interior angles

Theorem 4.2 Triangle Sum Theorem  The sum of the measures of the interior angles of a triangle are 180° m<1= m<2= m<3=

Theorem 4.3 Third Angles Theorem  If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent Theorem 4.4 The acute angles of a right triangle are complementary.

More Theorems Theorem 4.5 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. m<1= m<B + m<A

Thms. Cont. Theorem 4.6: Exterior Angle Inequality  The measure of an exterior angle of a triangle is greater than the measure of either of the two remote interior angles. m m<B or m<A

Finding Angle Measures