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34 Cards in this Set
- Front
- Back
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What are the three undefined ideas in geometry
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1. point: has no size, but can be represented by a dot.
2. line: has no thickness, and extends in two directions infinitely 3. plane: a figure that extends in all directions without ending, and has no edges |
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What is SPACE?
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Space is the set of all points.
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What are COLLINEAR POINTS?
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Collinear points are points all in one line.
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What are COPLANAR POINTS?
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Coplanar points are points all in one plane.
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What is the INTERSECTION OF TWO FIGURES?
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The intersection of two figures is the set of points that are in both figures.
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What is a SEGMENT?
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A segment consists of the end points of the segment and all points in between those points.
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What is RAY AC ->?
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Ray AC-> consists of segment AC and all points P such that C is between A and P. The endpoint of ray AC-> is A, the point named first.
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What is the LENGTH OF SEGMENT MJ?
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Segment MJ,denoted by MJ, is the distance between point M and point J.
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What is a POSTULATE OR AXIOM?
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A postulate or axiom is a statment that is accepted without proof.
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What is the RULER POSTULATE?
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The ruler postulate states:
1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once a coordinate system has been choosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. |
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What is the SEGMENT ADDITION POSTULATE?
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The segment addition postulate states:
If B is between A and C, then AB+AC=AC |
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What does the term CONGRUENT mean?
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Congruent means that two objects have the same size and shape.
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What are CONGRUENT SEGMENTS?
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Congruent segments are segments that have equal lengths.
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What is the MIDPOINT OF A SEGMENT?
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The midpoint of the segment is the point that divides the segment into two congruent segments.
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What is the BISECTOR OF A SEGMENT?
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The bisector of a segment is a line, segment, ray or plane that intersects the segment at its midpoint.
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What is an ANGLE?
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An angle is the figure that is formed by two rays with the same endpoint. The two rays are called the SIDES of the angle, and their common endpoint is called the VERTEX of the angle.
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What is an ACUTE ANGLE?
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An angle with a measure between 0 and 90.
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What is a RIGHT ANGLE?
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A right angle is an angle with a measure of 90.
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What is an OBTUSE ANGLE?
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An obtuse angle is an angle with a measure between 90 and 180.
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What is a STRAIGHT ANGLE?
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A straight angle is an angle with a measure of 180.
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What is the PROTRACTOR POSTULATE?
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The protractor postulate states:
On line AB in a given plane, choose any point O between A and B. Consider ray OA and ray OB and all the rays that can be drawn from O on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. ray OA is paired with 0 and ray OB is paired with 180. b. if ray OP is paired with x, and ray OQ is paired with y, the the measure of angle POQ is equal to the absolute value of x minus y. |
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What is the ANGLE ADDITION POSTULATE?
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The angle addition postulate states:
If angle AOB and angle BOC are adjacent then the sum of the measures of the smaller angles is equal to the measure of the larger angle. |
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What are CONGRUENT ANGLES?
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Congruent angles are angles that have equal measures.
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What are ADJACENT ANGLES?
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Adjacent angles are two angles in a plane that have a common vertex and a common side, but no common interior points.
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What is the BISECTOR OF AN ANGLE?
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The bisector of an angle is the ray that divides the angle into two congruent adjacent angles.
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Complete the postulate:
"A line contains..." |
A line contains at least two points, a plane contains at least three points not all in one line, space contains at least four points not all in one plane.
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Complete the postulate about lines:
"Through any two..." |
Through any two points there is exactly one line.
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Complete the postulate about planes:
" Through any three..." |
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
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Complete the postulate about lines and planes:
"If two points are..." |
If two points are in a plane than the line that contains the points is in that plane.
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Complete the postulate about the intersection of planes:
" If two..." |
If two planes intersect, then their intersection is a line.
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What are THEOREMS?
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Theorems are important statements that are proved.
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Complete the theorem about the intersection of lines:
" If two lines..." |
If two lines intersect, then they intersect in exactly one point.
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Complete the theorem about lines and noncollinear points:
" Through a line and..." |
Through a line and a point not on the line there is exactly one plane.
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Complete the theorem about lines and planes:
"If two lines..." |
If two lines intersect, then exactly one plane contains the lines.
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