Objective: Know and apply that if a line is perpendicular to each of two intersecting lines at point of intersection, the line is perpendicular to the plane determined by them

	1	Lines  and  intersect at point E.  Line m is perpendicular to lines  and  at point E.

Which statement is always true?
1)	Lines  and  are perpendicular.	
2)	Line m is parallel to the plane determined by lines  and .	
3)	Line m is perpendicular to the plane determined by lines  and .	
4)	Line m is coplanar with lines  and .	

	2	As shown in the diagram below,  and  intersect at point A and  is perpendicular to both  and  at A.

Which statement is not true?
1)	 is perpendicular to plane BAD.	
2)	 is perpendicular to plane FAB.	
3)	 is perpendicular to plane CAD.	
4)	 is perpendicular to plane BAT.	

3 Lines j and k intersect at point P.  Line m is drawn so that it is perpendicular to lines j and k at point P.  Which statement is correct?
1)	Lines j and k are in perpendicular planes.	
2)	Line m is in the same plane as lines j and k.	
3)	Line m is parallel to the plane containing lines j and k.	
4)	Line m is perpendicular to the plane containing lines j and k.	

	      4	Lines m and n intersect at point A.  Line k is perpendicular to both lines m and n at point A.  Which statement must be true?
1)	Lines m, n, and k are in the same plane.	
2)	Lines m and n are in two different planes.	
3)	Lines m and n are perpendicular to each other.	
4)	Line k is perpendicular to the plane containing lines m and n.	

	5	In plane P, lines m and n intersect at point A.  If line k is perpendicular to line m and line n at point A, then line k is
1)	contained in plane P	
2)	parallel to plane P	
3)	perpendicular to plane P	
4)	skew to plane P	

	6	Lines a and b intersect at point P.  Line c passes through P and is perpendicular to the plane containing lines a and b.  Which statement must be true?
1)	Lines a, b, and c are coplanar.	
2)	Line a is perpendicular to line b.	
3)	Line c is perpendicular to both line a and line b.	
4)	Line c is perpendicular to line a or line b, but not both.	

Objective: Know and apply that through a given point there passes one and only one plane perpendicular to a given line

	1	Point P is on line m.  What is the total number of planes that are perpendicular to line m and pass through point P?
1)	1	
2)	2	
3)	0	
4)	infinite	

	2	Point P lies on line m.  Point P is also included in distinct planes Q, R, S, and T.  At most, how many of these planes could be perpendicular to line m?
1)	1                                                   3) 3	
2)	2                                                   4) 4	

3   Point A is on line m.  How many distinct planes will be perpendicular to line m and pass through point A?
1)	one	
2)	two	
3)	zero	
4)	infinite	

Objective: Know and apply that through a given point there passes one and only one line perpendicular to a given plane

	1	Through a given point, P, on a plane, how many lines can be drawn that are perpendicular to that plane?
1)	1	
2)	2	
3)	more than 2	
4)	none	

	2	Point A is not contained in plane B.  How many lines can be drawn through point A that will be perpendicular to plane B?
1)	one	
2)	two	
3)	zero	
4)	infinite	

3  Point A lies in plane B.  How many lines can be drawn perpendicular to plane B through point A?
1)	one	
2)	two	
3)	zero	
4)	infinite	

Objective : Know and apply that two lines perpendicular to the same plane are coplanar

	1	If two different lines are perpendicular to the same plane, they are
1)	collinear	3)	congruent	
2)	coplanar	4)	consecutive	

Objective: Know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane

	1	If  is contained in plane P, and  is perpendicular to plane R, which statement is true?
1)	 is parallel to plane R.	
2)	Plane P is parallel to plane R.	
3)	 is perpendicular to plane P.	
4)	Plane P is perpendicular to plane R.	

	2	As shown in the diagram below,  is contained in plane R,  and  are contained in plane S, and , , and  intersect at A.

Which fact is not sufficient to show that planes R and S are perpendicular?
1)		
2)		
3)		
4)		

Objective: Know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane

	1	In the diagram below, line k is perpendicular to plane P at point T.

Which statement is true?
1)	Any point in plane P  also will be on line k.	3)	All planes that intersect plane P  will pass through T.	
2)	Only one line in plane P  will intersect line k.	4)	Any plane containing line k is perpendicular to plane P.	

	2	In the diagram below,  is perpendicular to plane AEFG.

Which plane must be perpendicular to plane AEFG?
1)	ABCE	3)	CDFE	
2)	BCDH	4)	HDFG	

Objective: Know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines

	1	In three-dimensional space, two planes are parallel and a third plane intersects both of the parallel planes.  The intersection of the planes is a
1)	plane	3)	pair of parallel lines	
2)	point	4)	pair of intersecting lines	

	2	Plane A  is parallel to plane B.  Plane C  intersects plane A in line m and intersects plane B in line n.  Lines m and n are
1)	intersecting	3)	perpendicular	
2)	parallel	4)	skew	

Objective: Know and apply that if two planes are perpendicular to the same line, they are parallel
	1	As shown in the diagram below,  intersects planes P, Q, and R.

If  is perpendicular to planes P and R, which statement must be true?
1)	Plane P  is perpendicular to plane Q.	
2)	Plane R  is perpendicular to plane P.	
3)	Plane P  is parallel to plane Q.	
4)	Plane R  is parallel to plane P.	

	2	Line k is drawn so that it is perpendicular to two distinct planes, P and R.  What must be true about planes P and R?
1)	Planes P and R are skew.	
2)	Planes P and R are parallel.	
3)	Planes P and R are perpendicular.	
4)	Plane P intersects plane R but is not perpendicular to plane R.	

	3	Plane R  is perpendicular to line k and plane D is perpendicular to line k.  Which statement is correct?
1)	Plane R  is perpendicular to plane D.	
2)	Plane R  is parallel to plane D.	
3)	Plane R  intersects plane D.	
4)	Plane R  bisects plane D.	

	4	If line  is perpendicular to distinct planes P and Q, then planes P and Q
1)	are parallel	
2)	contain line 	
3)	are perpendicular	
4)	intersect, but are not perpendicular	
5  If two distinct planes, A and B, are perpendicular to line c, then which statement is true?
1)	Planes A and B are parallel to each other.	
2)	Planes A and B are perpendicular to each other.	
3)	The intersection of planes A and B is a line parallel to line c.	
4)	The intersection of planes A and B is a line perpendicular to line c.	

	6	Plane A and plane B are two distinct planes that are both perpendicular to line .  Which statement about planes A and B is true?
1)	Planes A and B have a common edge, which forms a line.	
2)	Planes A and B are perpendicular to each other.	
3)	Planes A and B intersect each other at exactly one point.	
4)	Planes A and B are parallel to each other.	

	7	A support beam between the floor and ceiling of a house forms a 90º angle with the floor.  The builder wants to make sure that the floor and ceiling are parallel. Which angle should the support beam form with the ceiling?
1)	45º	
2)	60º	
3)	90º	
4)	180º