3.5 Parallel Lines and Triangles

Slides:

Advertisements

Similar presentations

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

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.

Parallel Lines and the Triangle Angle-Sum Theorem

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

Warm-Up  Find the value of x for which l || m. SWBAT use parallel lines to prove a theorem about triangles SWBAT find measures of angles of triangles.

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

Bellringer Find the slope going through the points. Use the given information to write an equation for each line.  1.  2. (2, 3), (  1,  6)  1. m=-2/3.

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

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

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

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

5.2 Exterior Angles of a Polygon

Triangles The three angles must add to 180 o. Exterior Angles.

3.4 parallel Lines and the Triangle Angle-Sum Theorem

Parallel Lines and the Triangle-Sum Theorem Learning Target: I can determine whether two lines are parallel.

3-3 Parallel Lines & the Triangle Angle Sum Theorem M11.B B Objectives: 1) To classify triangles and find the measures of their angles. 2) To.

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

DO NOW Bell Work – do 4 boxes on page 3 of note-taker While you are waiting for you computer/LEARN to log on… o TURN in Parallel City assignment o TURN.

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.

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

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

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

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

3-4 Parallel Lines and the Triangle Angle-Sum Theorem Objectives: 1) to classify triangles and find the measures of their angles 2) To use exterior angles.

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.

3 – 2 Ditto; HW Answers 8)x = 43 9)x = 90 10)x = 38 11)x = )x = 70 13) x = 48.

Do Now. Section 8.2 Angles in Polygons Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex polygon with n sides.

Lesson 5.2 Polygon Exterior Angle Sum HOMEWORK: 5.2/ 1-10.

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

Parallel Lines and Triangles Chapter 3 Section 5.

Warm Ups Classify each angle Classify each angle Solve Each Equation x= x+105= x + 58 = x = 90.

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

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.

Geometry Section 4.1 Apply Triangle Sum Properties.

4.2 Angles of Triangles Then: You classified triangle by their side or angle measures. Now: 1. Apply the Triangle Angle-Sum Theorem. 2. Apply the Exterior.

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

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Exterior Angle Theorem Parallel Lines Cut by a Transversal

Section 3-5 Parallel lines and Triangles.

Section 4-1 Triangles and Angles.

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

Name the type of triangle shown below.

3.5 Parallel lines and Triangles

11-4 Exterior Angles of Triangles

Angles of Triangles 4.2.

Exterior Angles of Triangles

3-3 & 3-4 Parallel Lines & the Triangle Angle-Sum Theorem

Types of Triangles and Their Properties

Triangle Application Theorems

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

Warm-up Find x a) b).

Exterior Angles of Triangles

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

Bellringer 3. slope 1/3 , y-intercept  (2, 3), (1, 6)

Triangle Theorems.

Parallel Lines and Triangles

Base Angles & Exterior Angles

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

Math Humor Q: How many feet are in a yard? A: It depends on how many people are in the yard!

Angles of Triangles Lesson #2 Pg. 19.

Angles of Triangles Lesson #2 Pg. 19.

Module 15: Lesson 1 Interior & Exterior Angles

Section 3-5 Parallel lines and Triangles.

Presentation transcript:

3.5 Parallel Lines and Triangles Parallel Postulate Through a point not on a line, there is one and only one line parallel to the given line.

Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180.

Using the Triangle Angle-Sum Theorem What are the values of x and y in the diagram?

Exterior Angle of a Polygon An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles.

Triangle Exterior Angles Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Using the Triangle Exterior Angle Theorem What is the measure of angle 1?

Using the Triangle Exterior Angle Theorem What is the measure of angle 2?

More Practice!!!!! Homework – p. 175 – 176 #9 – 19.