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

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

4-2 Angles of Triangles You classified triangles by their side or angle measures. Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

4.2 Angles of Triangles.

3.5 Parallel Lines and Triangles

Triangles. A triangle is a polygon with three sides.

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

3-5 Parallel Lines and Triangles. Classification by Sides (NOT in the book!) Equilateral TriangleIsosceles Triangle Scalene Triangle 3 congruent sides2.

Applying Triangle Sum Properties

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

Classify Triangles Standard 4C.

Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Classifying Triangles Angle Measures of Triangles.

6-1: Congruent Figures, Classifying Triangles, and Related Theorems

Section 2.7 PROVE ANGLE PAIR RELATIONSHIPS. In this section… We will continue to look at 2 column proofs The proofs will refer to relationships with angles.

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

1 Geometry Section 4-1B Angles Outside the Triangle Pg. 247 Be ready to grade 4-1A Quiz Friday.

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

Triangles and Angles Sec 4.1 GOALS: To classify triangles by their angles and sides To find missing angle measures in triangles.

3.4 parallel Lines and the Triangle Angle-Sum Theorem

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

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.

Triangles Geometry Mr. Zampetti Unit 3, Day 1. Today’s Objectives To learn new strategies that will help find the measures of angles in a triangle To.

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

Triangle Inequalities What makes a triangle and what type of triangle.

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

Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Geometry Section 4.1 Triangle Sum Theorem. A triangle is the figure formed by three line segments joining three noncollinear points. A B C.

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.

3.5 Parallel Lines and Triangles

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.

HONORS GEOMETRY 4.2. Angles of Triangles. Do Now: Classify the following triangles and then find x and ?.

Parallel Lines and Triangles Chapter 3 Section 5.

Applying Parallel Lines to Polygons Lesson 3.4 Pre-AP Geometry.

Chapter 3 Lesson 3 Objective: To use exterior angles of triangles.

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

Triangles The sum of the measures of the angles of a triangle is 180 degrees. m A + m B + m C = 180 o A BC An angle formed by a side and an extension.

Triangles Chapter What is the sum of the angles inside a triangle? 180º? Prove it m Given A B C Angle Addition Postulate/Definition of a Straight.

Geometry Section 4.1 Apply Triangle Sum Properties.

4.1 Triangle Angle Sum and Properties. How many degrees in a triangle? The sum of the angles in any triangle is exactly 180 degrees.

Angles of Triangles.

Section 4-1 Triangles and Angles.

Geometry 4.1 Triangle and Angles.

Angles of Triangles 4.2.

Exterior Angles of Triangles

Section 3-4 Angles of a Triangle.

5.5 Inequalities in One Triangle

Chapter 4: Congruent Triangles

Exterior Angles.

Prove Angle Pair Relationships

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

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.

Base Angles & Exterior Angles

Correcting Assignment #24 (6, 7, 11-15, 19-24, 27, 29, 31-32)

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.

3-3 Parallel Lines & the Triangle Angle Sum Theorem

4.1 – Apply triangle sum properties

5.2 Proving That Lines Are Parallel

Brett Solberg – AHS – ’11-’12

Bellwork Solve for the variable.

Module 15: Lesson 1 Interior & Exterior Angles

Presentation transcript:

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

Exterior Angle An exterior angle is formed by extending one of the side of the triangle. Exterior angle

Adjacent Interior Angle… The interior angle in a linear pair with an exterior angle. Adjacent interior angle An exterior angle

Remote Interior Angles The two angles that are away from the exterior angle. Exterior angle Remote interior angle

Try It 1.Name the exterior angles in the figure. 2. Name the remote interior angles for angle

What’s My Angle? You will need paper, a straight edge and a protractor. You will draw one of the following as instructed: Equilateral triangleIsosceles triangle Right triangleScalene Triangle Obtuse Triangle Draw an extension on one side and measure the exterior angle and the three interior angles.

Complete the Table. 83°40° 84°148° 71°54°

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

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

Theorems about Angles in Special Triangles Each angle of an equilateral triangle measures 60°. The acute angles of a right triangle are complementary.

What are remote interior angles? The two angles that are away from the exterior angle. What is the relationship between an exterior angle and the remote interior angles? The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Assignment 4-1B Page 250, 1-9, 13-15, 19-24