Unit 2 Lesson 5 Consturcting parallel and perpendicular lines

Question 1

midpoint

Answer 1

a point at the center or middle of a segment

Question 2

perpendicular

Answer 2

intersecting at a 90-degree angle

Question 3

perpendicular bisector

Answer 3

a line or line segment that divides another line segment into two equal parts and intersects it at a 90-degree angle

Question 4

right angle

Answer 4

an angle that measures exactly 90 degrees

Question 5

Describe the steps to construct a line that is perpendicular using the paper folding method.

Answer 5

Draw a line segment with endpoints A and B. Fold the piece of paper so that point A lands on the segment. When you unfold the piece of paper, draw a line segment along the fold. This line segment is perpendicular to line segment AB¯¯¯¯¯
.

Question 6

perpendicular symbol

Answer 6

The upside down “T” ( ⊥
) is a symbol for perpendicular.

Question 7

What are two key features of perpendicular bisectors?

Answer 7

A perpendicular bisector intersects a segment at a right angle (or 90-degree angle) and divides the segment into two equal but smaller segments.

Question 8

What steps would you take to construct a right triangle using the paper folding method?

Answer 8

: Draw a segment with endpoints A and B. Fold point A so that it lands on the line segment. Draw a segment along the fold going directly upward. Place a point at the end of the upward endpoint labeled C. Connect points B and C using a straightedge.

Question 8

Using a straightedge, a pencil, paper, and a compass, construct a perpendicular bisector.

Answer 8

Draw segment AB
and place the pointed end of a compass on point A. With the pencil end of the compass just past the center of the segment, draw an arc that extends both above and below the segment. Then, place the pointed end of the compass on point B without changing the distance and draw another arc that extends both above and below the segment. At the intersection of the two arcs, above and below the segment, place points. Finally, draw a line through the points using a straightedge.

Question 9

To make sure that two lines are a predetermined distance apart, which method would you use? Constructing a parallel line to another line? Or constructing a parallel line through a point not on the line?

Answer 9

You would use the method of constructing a parallel line through a point not on the line as this ensures that you can use a predetermined distance to construct this parallel line.

Question 10

Using a compass, straightedge, pencil, and a piece of paper, construct a line that is parallel to another line. Make sure to follow all the steps in the instructions.

Answer 10

• Construct a line and then construct another line that intersects the line.
• Place point A at the intersection of the two lines and then construct an arc that intersects both lines you have drawn.
• At the points of intersection of the arc with the two lines, place points C and B. Keeping the compass at the same distance, construct another arc by placing the pointed end at point C.
• This arc must be between the two lines you have constructed.
• Without changing the distance of the compass, place the pointed end at point B and construct another arc that intersects with the second arc you constructed. Draw a point at the intersection of the two rays labeled D.
• Draw a line using a straightedge through points C and D.