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M1 Perpendicular Transversals and Transitivity

Page history last edited by Cristian Brenner 10-5 13 years, 4 months ago

_____(0-10 pts) Describe the perpendicular transversal theorem. Give at least 3 examples.

by: Sangwoo Shin

 

Perpendicular Transversal Theorem ( also called the theorem 3-4-2)

Book Def: In a plane, if a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other line.

If a line( transversal) intersects two parallel lines and one of the parallel lines is perpendicular to the transversal then the other parallel line is also perpendicular to the transversal.

 

Proof this Theorem:

Given:YX ll WV , YWㅗWV

Prove: YWㅗYX

Proof:

 

More About Perpendicular Transversal Theorem

Amani Mubarak

 

This theorem states that if you have two parallel lines with a transversal, then the two lines will be perpendicular to the transversal.

 

     EXAMPLES: 

 

#1

#2



 

#3

True or False?

This picture represents defenitios of Perpendicular Transversals Theorem

 

 

FALSE: This picture doesnt apply to Perpendicular Transversals Theorem because line X and J are not parallel, so transversal

K is only perpendicular to line X.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_____(0-10 pts) Describe how the transitive property also applies to parallel and perpendicular lines. Include a discussion about theorems 3-4-3 and 3-4-1. Give at least 3 examples of each.

 

Mariana Botran:

 

 

The transitive property also applies to:

Parallel lines: if line A is parallel to line B and line B is parallel to line C, then line A is parallel to line C.

 

 

 

Perpendicular lines: If line A is perpendicular to line B and line B is perpendicular to line C, then line A is PARALLEL to line C.

 

 

 

 

Theorem 3-4-3: If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

 

 

Example 1:

Example 2:

 

 

Example 3:

 

Theorem 3-4-1: It two intersecting lines form a linear pair of congruent angles, then they are perpendicular.

 

Example 1:

 

Example 2:

Example 3:

The Transitice property says that when:

Parallel lines: If line 1 is parallel to line 2 and  line 2 is parallel to line 8, then line 1 is parallel to line 8.

 

The Transitive property says that when:

Perpendicular lines:If line 3 is perpendicular to line 4 and line 4 is perpendicular to line 7, then line 3 is parallel to line 7.

 

3-4-3:

It says that when to coplanar line are perpendicular to a line then that lines are parallel.

 

 

3-4-1:

If two intersecting lines form linear pair and angles formed are congruent, then they are perpendicular.

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