3-4 Parallel and perpendicular Lines

Students will be able to:◦ Define and apply theorems about parallel and

perpendicular lines◦ Relate parallel and perpendicular lines

Objectives

You can use relationships of two lines to a third line to decide whether the two lines are parallel or perpendicular to each other

Essential Understanding

If two lines are parallel to the same line, then they are parallel to each other.

Use this theorem to help prove lines are parallel

Theorem

What does it mean to be perpendicular? Symbolized by:

Perpendicular

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⊥

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Draw a picture of what this looks like. Use this theorem to help prove lines are

parallel

Theorem

A carpenter plans to install molding on the sides and the top of a doorway. The carpenter cuts the ends of the top piece and one end of each of the side pieces at 45 degree angles. Will the side pieces of molding be parallel? Explain

Problem 1

Can you assemble the pieces to form a picture frame with opposite sides parallel? Explain.

Problem 2

What is the relationship between segments AB and CD? Explain.

They are parallel because they are both perpendicular to segment BC.

Problem 3

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

Use this theorem to help prove lines are perpendicular

Theorem Perpendicular Transversal Theorem

In a plane, Prove:

Problem 4 Write a two column proof

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c⊥b,

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b⊥d,

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d⊥a

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c⊥a

In a plane, Prove: c||d

Problem 4 Write a paragraph proof.

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c⊥b,

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b⊥d,

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d⊥a

6-8, 17, 18, 20-24 even 8 Problems

Homework