Math 78 Pre Test

Math 78 Pre Test

Unit 7: Congruence

Knowledge and Understanding Math

1. What type of angles is between a set of parallel lines on opposite sides of a transversal?

2. Compare the relation of the slopes of perpendicular lines and parallel lines.

Proficiency of Skills

Use the figure to answer questions 3-5.

3. Name a pair of angles that are:

a.  Corresponding______

b.  Alternate interior______

c.  Vertical______

4.  Name a pair of angles that are:

d.  Alternate exterior______

e.  Same-side Interior______

f.  Supplementary______

5.  Determine the m and the m.

6.  Use the figure below to solve for x.

7.  Draw line CD and construct a perpendicular bisector.

8.  Construct an angle bisector of . Draw in the lines of the congruent triangles that are formed. Write a statement that shows that the 2 triangles are congruent.

9.  The equation of line a is y = ¼x + 2 and the equation of line b is y = -4x -5. Are the two lines parallel, perpendicular or neither? Explain.

Applications of Math

10.  Northland Builders are selling 3 home sites along the Etowah River. The lots are separated by parallel lines. If the total river frontage of the lots is 800 meters, find the river frontage for each lot.

11. Carpenters use parallel wall studs in building support walls. Describe two ways that a carpenter could guarantee that the wall studs BJ and CK are parallel.

A B C D E

F

G

H

I J K L M

12.  David is a contractor who is building a house diagonally on a corner lot. To see if the house will fit where he wants it, he has drawn a blue print. The exterior walls of the house are perpendicular. He wants to know if he drew it correctly. Would the walls be perpendicular if the corners of the walls where at the coordinates (2, 0), (4, 1), (2, 5), and (0, 4)? Why? Show all work.

Math 78 Unit 7 Pre Test Answers:

1. Alternate Interior Angles

2. Answers will vary: Slopes of parallel lines are the same; Slopes of perpendicular lines are opposite reciprocals.

a. 1,5; 3,z; 2,6; 4, 2z+30

b. 3,6; 4,5

c. 1,4; 2,3; 6,z; 5, 2z+30

d. 2,z; 1,2z+30

e. 3,5; 4,6

f. 1,2; 1,3; 2,4; 3,4; 5,6; 5,z; 6,2z+30; z,2z+30; 1,6; 2,5; 1,z; 2,2z+30

5. m=130; m=50

6. x = 4

7.

8.

ΔABDΔCBD

9. Perpendicular because the slopes are negative (opposite) reciprocals.

10. Respectively: 333 1/3 m; 266 2/3 m; 200 m

11. Answers will vary: corresponding angles are congruent; alternate exterior angles are congruent; alternate interior angles are congruent; consecutive interior angles are supplementary-angles could be named

12. Explanations will vary: Yes, the slopes are opposite reciprocals.