Geometry Chapter 3 Practice Test

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Geometry Chapter 3 Practice Test

1.

Identify a pair of parallel segments.

a.		c.
b.		d.

2.

Use the figure below.

For the cube shown,

and

are ___________.

a.	parallel lines	c.	skew lines
b.	oblique lines	d.	perpendicular lines

3.

Identify the statement as true or false and justify your answer.

Plane M is perpendicular to line s through point Q. Therefore it is the only plane perpendicular to s through point Q.

a.	False; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane.
b.	True; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane.
c.	True; Given a point on a line, there is one and only one plane perpendicular to the line through that point.
d.	False; Given a point on a line, there is one and only one plane perpendicular to the line through that point.

4.

Use the Corresponding Angles Converse and

to show that

.

a.	is given. From the diagram, and are corresponding angles. So by the Corresponding Angles Converse, .
b.	is given. From the diagram, and are alternate interior angles. So by the Alternate Interior Angles Converse, .
c.	By the Corresponding Angles Converse, . From the diagram, .
d.	is given. From the diagram, and are corresponding angles. So by the Corresponding Angles Theorem, .

5.

Which of the following can be concluded given

?

a.
b.
c.
d.

6.

Determine whether the lines shown are parallel, perpendicular, or neither.

a.	neither	c.	parallel
b.	perpendicular	d.	not enough information to tell

7.

The equations of four lines are given. Identify which lines are parallel.

Line 1:	y = x + 6
Line 2:	x + y = –6
Line 3:	y = x – 8
Line 4:	y + 7 = (x + 4)

a.	Lines 2 and 3 are parallel.	c.	All four lines are parallel.
b.	Lines 1 and 4 are parallel.	d.	Lines 1 and 2 are parallel.

8.

Identify the lines that are perpendicular:

;

;

;

a.	None of the lines are perpendicular.
b.	and are perpendicular.
c.	and are perpendicular.
d.	and are perpendicular; and are perpendicular.

9.

Write an equation in slope-intercept form for the line parallel to y =

x – 2 that passes through the point (8, –2).

a.	y = x +	c.	y = x –
b.	y = x –	d.	y = x – 2

10.

Find the point P along the directed line segment from point A(–18, –2) to point B(0, 6) that divides the segment in the ratio 1 to 3.

a.	P(, )	c.	P(, )
b.	P(, )	d.	P(, )

11.

Complete the statement with

, or no conclusion is possible.

If

, then .

12.

Complete the statement.

If

, then .

a.		c.
b.		d.	No conclusion is possible.

13.

Which lines, if any, can be proved parallel given the following diagram? For each conclusion, provide the justification.

14.

Which lines, if any, must be parallel based on the given diagram and information. Give the justification for each conclusion.

15.

Tell whether lines m and n are parallel or not parallel and explain.

16.

Given: and

.
Prove:

Proof:

State the justification for Step 3.

17.

Write an equation in slope-intercept form for the line that passes through

and is perpendicular to the line described by .

18.

Determine whether the line through

and

and the line through

and

are parallel, perpendicular, or neither.

19.

The point

partitions the directed segment from

to

in the ratio 2 to 3.
a. What are the coordinates of

?
b. Use slope to verify that

lies on

. Explain your answer.

20.

Complete this proof. Given: Lines q and r are parallel.
Transversal t intersects lines q and r.
Prove:

are supplementary.

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