Interior and Exterior Angles of a Triangle. What do we know about triangles? All three interior angles add to 180. The exterior angle is supplement (adds.

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

Triangles. A triangle is a polygon with three sides.

Interior and Exterior Angles of a Triangle. What do we know about triangles? All three interior angles add to 180. The exterior angle is supplement (adds.

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

Geometry 5 Level 1. Interior angles in a triangle.

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

Exterior Angle Theorem

3-5 Parallel Lines and Triangles

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.

Triangle Sum Properties & Inequalities in a Triangle Sections 4.1, 5.1, & 5.5.

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

The sum of the measure of the angles of a triangle is 1800.

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.

Angle Relationships in Triangles

4.1 & 4.2 A Notes. Type of ∆DefinitionPicture Equilateral Triangle CLASSIFICATION BY SIDES All sides are 

Polygons – Angles In Regular Polygons Regular Polygons have equal sides and equal angles, So if we can find one side, we would know the measure of all.

Angles of Polygons Find the sum of the measures of the interior angles of a polygon Find the sum of the measures of the exterior angles of a This scallop.

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.

Warm Up. Answer 7.1- Triangle Application Theorems Objective- apply theorems about interior angles, the exterior angles and the midlines of triangles.

Write a statement about the sum of the interior angles of a triangle below: The sum of all the interior angle in a triangle is 180 o

 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.

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

+ Angle Relationships in Triangles Geometry Farris 2015.

3-5 Parallel Lines and Triangles I can apply the triangle angle sum theorem to find the values of variables. I can apply the exterior angle theorem to.

4-1 Classifying Triangles SWBAT: Identify and classify triangles by angle measures and side measures. G.6.

 Scalene Triangle No sides congruent  Isosceles Triangle Exactly 2 sides congruent  Equilateral Triangle All sides congruent.

Angles of Triangles.

Measuring Angles in Triangles

Section 4-1 Triangles and Angles.

Name the type of triangle shown below.

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

Angles in polygons.

3.5 Parallel lines and Triangles

11-4 Exterior Angles of Triangles

Angles of Triangles 4.2.

Exterior Angles of Triangles

Angle CAB + Angle ACB + Angle ABC = 180 degrees

Angles in regular polygons

Properties of Triangles

Triangle Fundamentals

Aim: What’s outside the triangle?

Properties of Triangles

Triangle Application Theorems

Drawing Triangles.

Polygons – Angles In Regular Polygons

Warm-up Find x a) b).

Aim: What’s outside the triangle?

Exterior Angles of Triangles

Aim: What’s outside the triangle?

L J M K (2x – 15)0 x0 500.

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

Triangle Theorems.

Triangle Fundamentals

Base Angles & Exterior Angles

Triangle sum and exterior angles

Triangle sum property.

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

Converse Definition The statement obtained by reversing the hypothesis and conclusion of a conditional.

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

Exterior Angle Theorem

G9 - Congruence Postulates for Triangles

Aim: What’s outside the triangle?

5.2-Inequalities and Triangles

Presentation transcript:

Interior and Exterior Angles of a Triangle

What do we know about triangles? All three interior angles add to 180. The exterior angle is supplement (adds to 180) with the interior angle. a b c d

Example 1: Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 A B C D Consider: 80 + (3x – 4) + Angle BCA = 180 Angle BCA + (5x + 8) = 180 *Both statements have 180 and Angle BCA

Example 1: Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 A B C D Which means: 80 + (3x – 4) = 5x + 8 We say that the sum of two interior angles is equal to the exterior of the third (3x – 4) = 5x + 8 3x + 76 = 5x = 2x 34 = x

Example 2: The sum of two interior angles in a triangle, is equal to the exterior of the third F G HI Angle GHI = 7x + 9 Angle FGH = 60 Angle GFH = 4x + 12

Try the following in your notebooks: Angle BCD = 6x +12 Angle ABC = 70 Angle BAC = 4x + 18 A B CD X= ____ Angle BCD = _____ Angle BCA = ____