Using Postulates and Diagrams

Using Postulates and Diagrams

Postulate: Through any two points there exists exactly one line.

Postulate: A line contains at least two points.

Postulate: If two lines intersect, then their intersection is exactly one point.

Postulate: Through any three noncollinear points there exists exactly one plane.

Postulate: A plane contains at least threenoncollinear points.

Postulate: If two points lie in a plane, then the line containing them lies in the plane.

Postulate: If two planes intersect, then their intersection is a line.

b. a. a. If two lines intersect, then their intersection is exactly one point. b. If two planes intersect, then their intersection is a line. EXAMPLE 1 Identify a postulate illustrated by a diagram State the postulate illustrated by the diagram. SOLUTION

Sketch a diagram showing TVintersecting PQat point W, so that TWWV. Draw TVand label points Tand V. Draw point Wat the midpoint of TVMark the congruent segments. Draw PQthrough W. EXAMPLE 3 Use given information to sketch a diagram SOLUTION STEP 1 STEP 2 STEP 3

Which of the following statements cannot be assumed from the diagram? ABplane S CDplane T AFintersects BCat point B. No drawn line connects E, B, and D, so you cannot assume they are collinear. With no right angle marked, you cannot assume CDplane T. EXAMPLE 4 Interpret a diagram in three dimensions A, B, and Fare collinear. E, B, and Dare collinear. SOLUTION

Using Postulates and Diagrams