Lesson 1-3Lesson 1-3

PostulatesPostulates

Ohio Content Standards:Ohio Content Standards:

Ohio Content Standards:Ohio Content Standards:

• Formally define geometric figures.• Establish the validity of conjectures about

geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

• Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, and inductive and deductive reasoning.

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• Postulate 1-1 :Postulate 1-1 :

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• Postulate 1-1 :Postulate 1-1 :– Two points determine a unique line.Two points determine a unique line.

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• Postulate 1-2 :Postulate 1-2 :

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• Postulate 1-2 :Postulate 1-2 :– If two distinct lines intersect, then their If two distinct lines intersect, then their

intersection is a point.intersection is a point.

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• Postulate 1-3 :Postulate 1-3 :

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• Postulate 1-3 :Postulate 1-3 :– Three noncollinear points determine a Three noncollinear points determine a

unique plane.unique plane.

As shown below, points K, L, and M are noncollinear.

KM

L

As shown below, points K, L, and M are noncollinear.

• Name all of the different lines that can be drawn through these points.

KM

L

As shown below, points K, L, and M are noncollinear.

• Name all of the different lines that can be drawn through these points.

• Name the intersection of KL and KM.

KM

L

Name all of the planes that are represented in the prism.Name all of the planes that are

represented in the prism.

A

H

B

G

FE

DC

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• Postulate 1-4 :

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• Postulate 1-4 :– If two distinct planes intersect, then their

intersection is a line.

The figure shows the intersection of six planes.

AB

CD

E

FG

H

The figure shows the intersection of six planes.

AB

CD

E

FG

H

Name the intersection of planeABC and plane DEF.

Assignment:

Pgs. 21 & 2210-30 evens