'Angles converse' presentation slideshows

Chapter 3

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Chapter 3

Chapter 3. Perpendicular and Parallel Lines. Chapter Objectives. Identify parallel lines Define angle relationships between parallel lines Develop a Flow Proof Use Alternate Interior, Alternate Exterior, Corresponding, & Consecutive Interior Angles

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Parallel and Perpendicular Lines

Parallel and Perpendicular Lines. Geometry Chapter 3. This Slideshow was developed to accompany the textbook Larson Geometry By Larson , R., Boswell, L., Kanold , T. D., & Stiff, L. 2011 Holt McDougal Some examples and diagrams are taken from the textbook. Slides created by

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Parallel

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Lines and Angles

Lines and Angles. You will be able to identify relationships between lines and angles formed by transversals. Relationships between lines. Parallel Lines ? two lines that are coplanar and do not intersect. Skew Lines? lines that do not intersect and are not coplanar.

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2. Write the converse of the following statement. If it is raining, then Josh needs an umbrella.

1. Find the value of x. 32. ANSWER. If Josh needs an umbrella, then it is raining. ANSWER. 2. Write the converse of the following statement. If it is raining, then Josh needs an umbrella. ALGEBRA. Find the value of x that makes m n. = 65 o. (3 x + 5) o. 3 x. = 60. x. = 20.

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Geometry: Chapter 3

Geometry: Chapter 3. Ch. 3. 4: Prove Lines are Parallel Ch. 3.5 Using Properties of Parallel Lines. Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

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Section 14.3: Proving Lines are Parallel

Section 14.3: Proving Lines are Parallel. Objective: By following instructions, students will be able to: Prove that two lines are parallel. Corresponding Angles Converse. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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Corresponding Angles Postulate

Corresponding Angles Postulate. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1. 2. ?1 ? ?2. Alternate Interior Angles. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3. 4.

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Chapter 3.3 Notes: Prove Lines are Parallel

Chapter 3.3 Notes: Prove Lines are Parallel. Goal: You will use angle relationships to prove that lines are parallel. Postulate 16 Corresponding Angles Converse : If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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GOAL

3.4. Proving Lines are Parallel. PROVING LINES ARE PARALLEL. 1. GOAL. The postulate and theorems learned in Section 3.3 all had the same hypothesis: Parallel lines are cut by a transversal. Now we will prove the converses to be true, and use them to prove lines are parallel. EXAMPLE 1.

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September 29, 2014

September 29, 2014. Take out your homework, do not turn in Get ready for a warm-up. Warm-up.

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EXAMPLE 3

Prove that if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. ? 4 ? 5. GIVEN :. g h. PROVE :. EXAMPLE 3. Prove the Alternate Interior Angles Converse. SOLUTION. REASONS. STATEMENTS. 1. g h. 1. Given. 2. 2.

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Essential Question

Essential Question. What postulate(s) can be used for the diagram?. Parallel Lines, Transversals and Angles. Corresponding Angles Postulate- If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Angles 1 and 5 are congruent

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Lesson

Proving Lines Parallel. Lesson. Ways to Prove Two Lines Parallel. Show that corresponding angles are equal (Corresponding Angles Converse) Show that alternative interior angles are equal (Alternate Interior Angles Converse)

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EXAMPLE 2

Snake Patterns. How can you tell whether the sides of the pattern are parallel in the photo of a diamond-back snake?. EXAMPLE 2. Solve a real-world problem. SOLUTION. Because the alternate interior angles are congruent, you know that the sides of the pattern are parallel. ANSWER.

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