Lesson 4-2 Angles of Triangles. Ohio Content Standards:

Slides:

Advertisements

Similar presentations

Warm Up Determine the measure of the missing interior angle. What type of triangle is it? Unit 8 - Lesson 2 Exterior Angles of a Triangle.

Advertisements

Lesson 3-4 (Parallel & Perpendicular Lines) perpendicula r parallel.

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.

4.2 Angles of Triangles.

3.5 Parallel Lines and 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.

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.

Lesson 4-3 Congruent Triangles. Ohio Content Standards:

Proving Angle Relationships

Lesson 5-1 Classifying Triangles. Ohio Content Standards:

Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Lesson 6-6 The Pythagorean Theorem. Ohio Content Standards:

Postulates and Paragraph Proofs

Lesson 2-6 Algebraic Proofs. Ohio Content Standards:

Lesson 2-7 Proving Segment Relationships. Ohio Content Standards:

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

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

Lesson 2-4 Deductive Reasoning. Ohio Content Standards.

Lesson 6-3 Similar Triangles. Ohio Content Standards:

Lesson 2-1 Inductive Reasoning and Conjecture. Ohio Content Standards:

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

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.

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Lesson 5-4 The Triangle Inequality. Ohio Content Standards:

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

Lesson 3-2 Angles and Parallel Lines. Ohio Content Standards:

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.

Lesson 4-6 Isosceles Triangles. Ohio Content Standards:

Parallel Lines and Triangles Chapter 3 Section 5.

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.

+ Angle Relationships in Triangles Geometry Farris 2015.

Use isosceles and equilateral triangles

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Section 3-5 Parallel lines and Triangles.

Angles of Triangles.

Measuring Angles in Triangles

Geometry 4.1 Triangle and Angles.

Angles of Triangles 4.2.

Exterior Angles of Triangles

4.2 Angles of Triangles Theorem 4-1: Angle Sum Theorem

Warm-up Find x a) b).

Class Greeting.

Exterior Angles of Triangles

Inside angles theorem.

Warm-up Find x a) b).

Warm-up Find x a) b).

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)

Triangle sum property.

Isosceles Triangles. Isosceles Triangles Base Angles If 2 angles in a triangle are congruent, then the sides opposite them are congruent.

Isosceles Triangles. Isosceles Triangles Base Angles If 2 angles in a triangle are congruent, then the sides opposite them are congruent.

Exterior Angle Theorem

Proving Congruence – SSS, SAS

Vertical Angles, Linear Pairs, Exterior Angles

Angle Relationships in Triangles

Module 15: Lesson 1 Interior & Exterior Angles

Section 3-5 Parallel lines and Triangles.

Presentation transcript:

Lesson 4-2 Angles of Triangles

Ohio Content Standards:

Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two- dimensional figures and three- dimensional objects.

Theorem 4.1 Angle Sum Theorem

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

Find the missing angle measures. 43° ° 79°

Theorem 4.2 Third Angle Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

Exterior Angle

Angle formed by one side of a triangle and the extension of another side.

Exterior Angle Angle formed by one side of a triangle and the extension of another side. 1

Remote Interior Angles

Interior angles of the triangle not adjacent to a given exterior angle.

Remote Interior Angles Interior angles of the triangle not adjacent to a given exterior angle. 2 3

Theorem 4.3 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.

Find the measure of each numbered angle in the figure ° 38° 32° 41° 64°

B 20° C A

Assignment: Pgs all, evens