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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. Examples. B. Determine whether the following statement is always, sometimes, or never true. Explain.
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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
Examples B.Determine whether the following statement is always, sometimes, or never true. Explain. • Plane BCG is the only plane containing FG and point C. • BF and FG intersect at FH. • FH is contained in the plane FGH. • Planes ADH and EFG intersect at EH. D A B C H E F G
ExamplesDetermine if each statement is true or false. Explain • If AB and BC intersect, then they intersect at B. • It is possible for two planes to intersect in exactly one point. • Three points always lie in exactly one plane. • If C is the midpoint of XY, then XC CY. • Congruent angles have a sum 180o. • If TP bisects RTO, then RTP and PTO are congruent.
Given: 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. Prove: ACD is a plane.
