3.4 Proofs with Perpendicular Lines

​3.4 Proofs with Perpendicular Lines

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Multiple Choice

Theorem 3-10: Perpendicular Transversal Theorem

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

• Parallel

• Perpendicular

• Not Enough Information

• Skew

Multiple Choice

How do you know that $$g\parallel h$$  ?

• Linear Pair Perpendicular Theorem

• Lines Perpendicular to a Transversal Theorem

• Corresponding Angles Theorem

• Definition of Congruent Angles

Multiple Choice

Determine which lines, if any, must be parallel.

• $$a\parallel b$$

• $$c\parallel d$$

• $$a\parallel e$$

• None of the lines are parallel.

Multiple Choice

Determine which lines, if any, must be parallel.

• $$l\parallel m$$

• $$n\parallel p$$

• $$m\parallel p$$

• None of the lines are parallel.

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Multiple Choice

The Parallel Postulate (3.1) states: If there is a point not on the line, then ________________.

• there is exactly one line through the point parallel to the given line.

• there are many lines through the point parallel to the given line.

• there is exactly one line through the point perpendicular to the given line.

• there are many lines through the point perpendicular to the given line.

Multiple Choice

The Perpendicular Postulate (3.2) states: If there is a point not on the line, then ________________.

• there is exactly one line through the point parallel to the given line.

• there are many lines through the point parallel to the given line.

• there is exactly one line through the point perpendicular to the given line.

• there are many lines through the point perpendicular to the given line.

Multiple Choice

What is the shortest distance between a point and a line?

• The length of the perpendicular segment from the point to the line.

• The length of the parallel segment from the point to the line.

• The circumference of the semi-circle from the point to the line.

• None of the above.

Multiple Choice

Find the distance from point P to $$\overline{AB}$$  .

• 16 units

• 5.7 units

• 32 units

• 6.8 units

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Multiple Choice

Given: $$<1\cong<2$$  

What statement is NOT true?

• $$m<1=m<2$$  

• $$m<1=90\degree$$  

• $$g\perp h$$  

• $$m<2=110\degree$$  

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Multiple Choice

Andrea constructs perpendicular lines (as shown at right). What basic construction is used to construct perpendicular lines?

• Copy a segment.

• Perpendicular Bisector

• Copy an angle

• Angle Bisector

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Multiple Choice

Multiple Choice

What geometric construction is shown in the diagram below?

• an angle bisector

• a line parallel to a given line

• an angle congruent to a given angle

• a perpendicular bisector of a segment

Multiple Select

Based on the construction above which of the following are always true, choose all that apply.

HINT: WHAT ARE THE PROPERTIES OF A PERPENDICULAR BISECTOR...

• AB=CD

• AE=EB

• CE=ED

• AC=BC