_____(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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