Euclidean Geometry

Which distance measures 7 units?

the distance between points M and P

Which is a mathematical statement consisting of a hypothesis and conclusion that has to be proven true?

theorem

Use the given diagram to answer the question. Which line is the intersection of two of the planes shown? Which line intersects one of the planes shown? Which line has points on three of the planes shown?

x z y

Which statements are true regarding undefinable terms in geometry? Check all that apply.

A point has no length or width. A point indicates a location in a coordinate plane. A plane consists of an infinite set of lines. A line consists of an infinite set of points.

Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R

A, B, D, E

Which statements are true regarding undefinable terms in geometry? Select two options. A point's location on the coordinate plane is indicated by an ordered pair, (x, y). A point has one dimension, length. A line has length and width. A distance along a line must have no beginning or end. A plane consists of an infinite set of points.

A, E

Exactly how many planes contain points J, K, and N?

1

How many planes exist that pass through points A, B, and C?

1

Points J and K lie in plane H. How many lines can be drawn through points J and K?

1

According to the number line, what is the distance between points A and B?

14 units

Which statements are true? Select three options. There are exactly two planes that contain points A, B, and F. There is exactly one plane that contains points E, F, and B. The line that can be drawn through points C and G would lie in plane X. The line that can be drawn through points E and F would lie in plane Y. The only points that can lie on plane Y are points E and F.

2, 3, 4

In a geometry class, students are asked to describe the dimensions of a plane based on the components that create a plane. Which student's response is correct? Mark states that a plane has zero dimensions because it is made up of three noncollinear points. Stacy states that a plane has two dimensions because it is made up of an infinite number of lines. Dewayne states that a plane has one dimension because it contains the line intersecting two points. Candice states that a plane can have multiple dimensions depending on how many points are labeled.

B. Stacy states that a plane has two dimensions because it is made up of an infinite number of lines.

Which diagram represents the postulate that states exactly one line exists between any two points?

C

Match the building block of geometry to the statement that defines it.

Definition - a formal statement declaring the meaning of a word Diagram - a visual tool representing mathematical ideas to be interpreted Postulate - a mathematical statement taken as fact theorem - a mathematical statement proven using postulates and definitions

Points W, K, and _________ are collinear. Line CA and line YK intersect at __________ Point _______ is not contained on line m.

J point B W

The three collinear points on line m are _________ Point _______ is not on line m. __________ line(s) could be drawn through points P and

J, K, and W Y One

Which undefined geometric term can be described as a one-dimensional set of points that has no beginning or end?

Line

The intersection of plane A and plane S will be _________ The intersection of lines n and k is _________ Point X is the intersection of _______

Line CW Point V line m and Plane A

Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points.

One plane can be drawn so it contains all three points.

Which undefined geometric term is described as a two-dimensional set of points that has no beginning or end?

Plane

Explain why there must be at least two lines on any given plane.

Sample Response: There exists one plane through any three noncollinear points. Since the points cannot be on the same line, at least two lines would have to pass through any of the three points.

Which statement is true about the points and planes? The line that can be drawn through points C and D is contained in plane Y. The line that can be drawn through points D and E is contained in plane Y. The only point that can lie in plane X is point F. The only points that can lie in plane Y are points D and E.

The line that can be drawn through points D and E is contained in plane Y.

Brook states that the distance on the line is 4 units. Caleb states that the whole line does not have a distance because it continues on forever. Vivian states that the line is 6 units long.

What distance did Brooke measure? Between L and M What distance did Vivian measure? Between M and N

Which describes the intersection of line m and line n? point W point X point Y point Z

point W

Which points are coplanar and noncollinear? points A and D points C and D points A, C, and D points A, B, and D

points A,B, and D