2.5 Postulates and Paragraph Proofs

Postulate- (also called an axiom) a statement that is accepted as true

Theorem- a statement or conjecture that has been shown/proven to be true

B. Determine whether the following statement is always, sometimes, or never true. Explain.a. Plane BCG is the only plane containing FG and point C.

b. BF and FG intersect at FH.

c. FH is contained in the plane FGH.

d. Planes ADH and EFG intersect at EH.

E

F G

H

C

D

BA

Examples

ExamplesDetermine if each statement is true or false.

Explain

1. If AB and BC intersect, then they intersect at B.

2. It is possible for two planes to intersect in exactly one point.

3. Three points always lie in exactly one plane.

4. If C is the midpoint of XY, then XC CY.

5. Congruent angles have a sum 180o.

6. If TP bisects RTO, then RTP and PTO are congruent.

Given:

Prove: ACD is a plane.

Proof: and must intersect at C because if two lines intersect, then their intersection is exactly one point. Point A is on and point D is on . Points A, C, and D are not collinear. Therefore, ACD is a plane as it contains three points not on the same line.

Example

Given: AB11111111111111

is the angle bisector of CAD. Prove: CAB DAB