Geometry 1.2 and 1.3 Brit Caswell.

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Presentation transcript:

Geometry 1.2 and 1.3 Brit Caswell

A point indicates a location and has no size.

A line contains infinitely many points. A line is represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points.

A plane consists of infinitely many lines. A plane is represented by a flat surface that extends without end and has no thickness. A plane consists of infinitely many lines.

Segment A segment is part of a line that consists of two endpoints and all points between them.

Ray A ray is part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.

Postulate 1.1 (pg 13) Through any two points there is exactly one line that passes through both points.

Postulate 1.2 (Pg 13) If two distinct lines intersect, then they intersect in exactly one point. Q: What if the lines are not distinct?

Postulate 1.3 (Pg 14) If two distinct planes intersect, then they intersect in exactly one line.

Through any three noncollinear points, there is exactly one plane. Postulate 1.4 (Pg 15) Through any three noncollinear points, there is exactly one plane.

Postulate 1.5 (Ruler Post., pg 20) Every point on a line can be paired with a real number. This makes a one-to-one correspondence between the points on the line and the real numbers. The real number that corresponds to a point is called the coordinate of the point.

This means, that if there are two segments, they can be added together This means, that if there are two segments, they can be added together. (See Post 1.6 Segment Addition Postulate)

Because segments have defined lengths, they can be bisected (cut in half), at their midpoint (the point at the middle of the segment). This creates two congruent (equal) segments.

I do (Pg 23, #4) The following two segments are congruent. Find the value of x. A M B 6x-7 5x+1

We Do (Pg 22, #3) Are AC and BD congruent?

You Do (Exit Ticket) Pg 21, #2 If EG = 59, what are EF and FG? E F G 8x-14 4x+1