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Postulate 7 (The parallel postulate)

Theorem 17

Corollary 1 to theorem 17

Corollary 2 to theorem 17

Through a point not on a line, there is exactly 1 line paralle…

Equal corresponding angles mean that lines are parallel

Equal alternate interior angles mean that lines are parallel

Supplementary interior angles on the same side of a transversa…

Rigid motion

Translation

Vector

Reflection

A transformation that preserves distance and angle measures.…

Sliding or moving an image... It is a rigid motion

Looks like an arrow, has direction and magnitude(length)... Used…

Flipping an image... Is a rigid motion... It does not preserve orien…

octahedral, octahedral, 90

octahedral, square pyramidal, 90, 180

octahedral, square planar, 90, 180

trigonal bipyramidal, trigonal bipyrami…

What shapes is this?... What angles?

What shapes is this?... What angles?

What shapes is this?... What angles?

What shapes is this?... What angles?

Prove they are Parralel

Theorem 18

Theorem 19

Corollary 1

Theorem 17-Equal corresponding angles mean that lines are para…

In a plane, two lines parallel to a third line are parallel to…

Parallel lines form equal corresponding angles.

Parallel lines form equal alternate interior angles.

Polis

Socrates

Plato

Aristotle

City-state form of government used in Greece 800-400BCE

Late 5th cBCE Athenian philosopher; Urged rational reflection…

Socrates' greatest pupil; Suggested humans could approach unde…

384 - 322 BCE, Greek philosopher; Alexander the Great's teache…

What the Symbols Mean

Linear Pair Theorem

Congruent Supplements Theorem

Right Angles Congruent Theorem

{=} - means that it is Congruent... * - is the symbol for degrees

If two angles form a linear pair, then they are supplementary

If two angles are supplementary to the same right angle(or to…

All right angles are congruent

Triangle

Congruence for Segments

Congruence for Angles

Congruence for Triangles

A ________ is the union of three segments (sides) whose end po…

Segment AB congruent with Segment XY iff AB = XY.

<ABC congruent with <XYZ iff m<ABC = m<XYZ.

If, under some correspondence between the vertices of two tria…

trigonal planar

trigonal planar

trigonal planar

bent trigonal planar

3 bonding, 0 lone pairs, 120 degree angles, geometry of electr…

3 bonding, 0 lone pairs, 120 degree angles, geometry of atoms

2 bonding, 1 nonbonding, slightly less than 120 degree angles,…

2 bonding, 1 nonbonding, slightly less than 120 degree angles,…