# Worksheet: Points, Lines, and Planes in Space

In this worksheet, we will practice identifying and modeling geometric concepts like points, lines, and planes in space along with their properties.

Q1:

State whether the following is true or false: Two coplanar lines perpendicular to the same line will always intersect each other.

• Afalse
• Btrue

Q2:

Complete the following: Two skew lines are two lines that .

• Alie in the same plane and do not have a common point
• Bintersect but do not lie in the same plane
• Care parallel
• Ddo not lie in the same plane and do not intersect
• Elie in the same plane and have a common point

Q3:

How many planes can pass through three non-collinear points?

Q4:

In what line do planes and intersect? • A
• B
• C
• D
• E

Q5:

What is the intersection of the plane through and the plane through ? • A
• B
• C
• D

Q6:

Complete the following: Two intersecting lines are two lines that .

• Ado not lie in the same plane
• Blie in the same plane and do not have a common point
• Clie in the same plane and have a common point
• Dare perpendicular
• Eare parallel

Q7:

What is the intersection of planes , , and ? • A
• B
• C
• D

Q8:

What is the intersection between segment and the plane ? • A
• B
• C
• D

Q9:

What is the intersection of the planes and ? • A
• B
• Cthe plane
• Dthe plane

Q10:

Determine the intersection of plane and plane and plane . • A
• B
• C
• D

Q11:

Observe the following figure and choose. • AThe straight line is contained within the plane.
• BThe straight line is intersected with the plane.
• CThe straight line is parallel to the plane.

Q12:

Observe the following figure and choose. • AThe straight line is parallel to the plane.
• BThe straight line is contained within the plane.
• CThe straight line is intersected with the plane.

Q13:

and are planes that intersect at line . is a point on line and is a point on plane . Which of the following are true? • A
• B
• C
• D

Q14:

and are planes that intersect at line . and are points on line and is a point on plane . Which of the following statements hold? • A
• B
• C
• D

Q15:

and are planes that intersect at line . is a point on plane and is a point on plane . Determine the intersection of plane with plane . • A
• B
• C
• D

Q16:

Complete: If is parallel to the plane , then .

• A
• B
• C

Q17:

Describe what is shown in the figure. • AA plane intersected by
• BA plane intersected by
• CA plane intersected by

Q18:

There are two parallel planes, and . A line intersects the planes and at points and respectively. The plane contains . Which figure matches the description?

• A • B • C Q19:

Which of the following is a line containing the point ? • A
• B
• C
• D
• E

Q20:

Which of the following is a line containing the point ? • A
• B
• C
• D
• E

Q21:

Which of the following is a line containing the point ? • A
• B
• C
• D
• E

Q22:

Which of the following is a line containing the point ? • A
• B
• C
• D
• E

Q23:

Which of the following lines contains the point ? • A
• B
• C
• D
• E

Q24:

Consider the following figure. Write another name for the plane .

• APlane
• BPlane
• CPlane
• DPlane
• EPlane

How many planes are shown in the figure?

Which two planes intersect in ?

• APlane and plane
• BPlane and plane
• CPlane and plane
• DPlane and plane
• EPlane and plane

Are planes and parallel or intersecting?

• BThey are intersecting.
• CThey are parallel.

Q25:

and are planes which intersect at line . Which of the following holds? • A
• B
• C
• D