2.3 Postulates and Diagrams

2.3 Postulates and Diagrams

by Mary Lett

​Objective and Standards

• ​Students will be able to identify postulates using diagrams, sketch and interpret diagrams.

• ​​HSG-CO.C.9: Prove theorems about lines and angles.

​Point and Line Postulates

Multiple Choice

2 lines intersect at a point

• always

• sometimes

• never

• Only when I wear a striped sweater

Multiple Choice

For any two points, there is a unique line through them

• always

• sometimes

• never

Multiple Choice

A line must have at least 2 points.

• Always

• Sometimes

• Never

Fill in the Blank

State the postulate illustrated by the diagram.

​Point and Plane Postulates

Multiple Choice

Complete the Three Point Postulate:

"Through any three noncollinear points, there exists exactly____________________"

• one plane

• one point

• two planes

• 6 points

Multiple Choice

Complete the Plane-Point Postulate:

"A plane contains ____________________"

• at least two noncollinear points

• at least three noncollinear points.

• no more than 3 noncollinear points

• none of the above

​Plane and Line Postulates

Multiple Choice

Complete the Plane-Line Postulate:

"If two points lie in a plane, then the line containing them ____________________"

• lies in the plane.

• is perpendicular to the plane

Multiple Choice

Complete the Plane-Intersection Postulate:

"If two planes intersect, then their intersection is ____________________"

• a plane.

• a line

• a circle

• a triangle

Fill in the Blank

State the postulate illustrated by the diagram.

​Vocabulary

• ​A line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at a point.

Multiple Select

Which of the following cannot be assumed from the diagram?

• Points A, B, and F are collinear.

• Points E, B, and D are collinear