3.5 Parallel lines and Triangles

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.

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

PARALLEL LINES AND TRANSVERSALS. CORRESPONDING ANGLES POSTULATE Two lines cut by a transversal are parallel if and only if the pairs of corresponding.

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

Objective: After studying this section, you will be able to apply theorems about the interior angles, the exterior angles, and the midlines of triangles.

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°

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Warm-Up x + 2 3x - 6 What is the value of x?. Geometry 3-3 Proving Lines Parallel.

PROVING LINES PARALLEL. CONVERSE OF  … Corresponding Angles Postulate: If the pairs of corresponding angles are congruent, then the lines are parallel.

3.3 Paragraph and Flow Proofs Warm-up (IN) Learning Objective: to write and understand mathematical proofs and to use mathematical reasoning to prove that.

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

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.

Lesson 2-5: Proving Lines Parallel 1 Lesson Proving Lines Parallel.

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

 4.1 Classifying Triangles. Example 1 Example 2.

3.5 Parallel Lines and Triangles

The Elements Definition 10 When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is.

Parallel Lines and Triangles Chapter 3 Section 5.

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.

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

Exterior Angle Theorem Parallel Lines Cut by a Transversal

Section 3-5 Parallel lines and Triangles.

Angles of Triangles.

Parallel Lines and Planes

Measuring Angles in Triangles

Section 4-1 Triangles and Angles.

3.4 Parallel Lines and Transversals

Name the type of triangle shown below.

3.2- Angles formed by parallel lines and transversals

Angle Theorems for Triangles

11-4 Exterior Angles of Triangles

Angles of Triangles 4.2.

Exterior Angles of Triangles

A C B Triangle Sum Theorem (4.1)

11.2 Angle Theorems for Triangles

Proving Lines Parallel

Entry Task 3. Draw a large scalene triangle on the sheet of yellow copy paper. Then cut it out. We will be using the triangles for our lesson today.

10/26 WORKBOOK WARM UP Exploring Interior Angles of Triangles– Open your workbooks to P. 351 EXPLORE: A-C!!! Parts A – H.

Warm-up Find x a) b).

Exterior Angles of Triangles

3.2- Angles formed by parallel lines and transversals

Congruent, Supplementary, and Complementary

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

Module 1- Lesson 7 and 8 Finding Unknown Angle Measures – Transversals and Auxiliary Lines Finding Unknown Angle Measures in Triangles.

Parallel Lines, Transversals, Base Angles & Exterior Angles

Triangle Theorems.

Parallel Lines and Triangles

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.

Triangle sum and exterior angles

Triangle sum property.

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

Exterior Angle Theorem

3-3 Parallel Lines & the Triangle Angle Sum Theorem

Vertical Angles, Linear Pairs, Exterior Angles

5.2-Inequalities and Triangles

Module 15: Lesson 1 Interior & Exterior Angles

Prove that the interior angles of a triangle have a sum of 180º

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

Section 3-5 Parallel lines and Triangles.

Presentation transcript:

3.5 Parallel lines and Triangles

Parallel lines help with triangle postulates. 55° 87° 38°

Triangle Sum Theorem All interior angles of a triangle add to 180°.

Ex 1 X= 87° 38° x°

Ex 2 X=____ ∠A=_____ ∠B=_____ A x+3° 22° x°+11 C B

Ex 3 If all three interior angles of a triangle have the ratio1:2:3 Draw the picture . Then find all angles.

Triangles have exterior angles. Angle M is an exterior angle. m

Exterior Angle Theorem Any exterior angle is equal to the sum of the non-connected interior angles. ∠1+ ∠2= ∠3 3 1 2

Ex 4 Find angle M. and x x 65° m 75°

H.W pg 175 1-5 odd, 9-13 all, 16-18all 22-24 all, 29-30