3-6
PART 2
Constructing Parallel
and Perpendicular Lines
Vocabulary
Review
Underline the correct word to complete each sentence.
1. A polygon cannot have parallel / skew sides.
2. Parallel / Skew lines are noncoplanar.
3. A transversal intersecting two parallel / skew lines forms pairs of congruent angles.
Use the diagram at the right for Exercises 4–9. Write parallel or skew to
describe each pair of segments.
4. BC and UT
5. BC and AD
B
A
6. BC and RU
D
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
8. RS and AD
T
S
R
7. RS and UT
C
U
9. RS and BC
Vocabulary Builder
quadrilateral
quadrilateral (noun) kwah drih LAT ur ul
Definition: A quadrilateral is a polygon with four sides and
four angles.
Examples: rectangle, square, parallelogram, trapezoid
Non-Examples: triangle, octagon, circle, hexagon
Use Your Vocabulary
10. Circle the quadrilateral(s).
165
Lesson 3-6, Part 2
Problem 3
Perpendicular at a Point on a Line
* )
* )
* )
* )
Got It? Use a straightedge to draw EF . Construct FG so that FG ' EF at point F.
11. Use the diagram at the right. Write each construction step.
G
Step 1
_________________________________________
E
F
H
Step 2
_________________________________________
_________________________________________
_________________________________________
Step 3
_________________________________________________________________
_________________________________________________________________
Step 4
_________________________________________________________________
_________________________________________________________________
Step 5
Postulate 3-4 Perpendicular Postulate
Complete the statement of Postulate 3-4 below.
12. Through a point not on a line, there is one and only one line parallel / perpendicular
to the given line.
13. Circle the diagram that models Postulate 3-4.
P
Chapter 3
P
P
166
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
_________________________________________________________________
Problem 4 Perpendicular From a Point to a Line
* )
* )
* )
* )
* )
Got It? Draw a line CX and a point Z not on CX . Construct ZB so that ZB ' CX .
Underline the correct word(s) to complete each sentence.
14. Open your compass to a size equal to / greater than the distance from Z to line /.
15. With the compass tip on point Z, draw an arc that intersects line / at one / two point(s).
16. Label the point(s) C and X / Z .
17. Place the compass point on C / Z
and make an arc below line /.
Z
18. With the same opening and the
compass tip on C / X , draw an
arc that intersects the arc you
made in Exercise 17. Label the
point of intersection B.
E
* ) * )
19. Draw ZB / CX .
20. Now construct a line through
point Z perpendicular to line /.
Lesson Check • Do you UNDERSTAND?
* )
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
In constructing the perpendicular to line AB at point P, is AC congruent to BC?
Explain.
21. Are the arcs at point C made with different compass openings?
Yes / No
C
P
A
22. Is AC congruent to BC? Explain.
B
___________________________________________________________________________
___________________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
construction
parallel
perpendicular
Rate how well you can construct parallel and perpendicular lines.
Need to
review
0
2
4
6
8
Now I
get it!
10
167
Lesson 3-6, Part 2