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A mathematical statement that can be proven |
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If two angles are right angles, then they are congruent. |
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If two angles are straight angles, then they are congruent |
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If a point (etc.) divides a segment into two congruent segments: -then it bisects the line -then it is the midpoint If a point bisects a segment, then it divides the segment into 2 congruent segments. If a point is a midpoint of a segment, then it divides the segment into 2 congruent segments If a point is the midpoint, then it bisects the segment. |
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If a ray divides an angle into 2 congruent angles, then it bisects the angle If a ray bisects an angle, then it divides the angle into 2 congruent angles |
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If two rays divide an angle into 3 congruent angles, then they bisect the angle If two rays bisect an angle, then they divide the angle into 3 congruent angles |
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What we can assume about lines/angles/etc. |
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-straightness of lines -collinearity of points -betweenness of points -relative positions of points |
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What we cannot assume about lines/angles/etc. |
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-if the angle is a right angle -congruent segments -congruent angles -relative size of segments/angles |
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If 2 angles or segments have the same measure, then they are congruent If 2 angles or segments are congruent, then they have the same measure |
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An angle that is >90 and <180 |
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An angle that is >0 and <90
If an angle is acute then it's angle measure is greater than 0 and less than 90 If an angle measure is greater than 0 and less than 90, then it's an acute angle |
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If an angle's measure is exactly 90, then it is a right angle If an angle is a right angle, then it's measure is exactly 90 |
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The union of 2 rays with a common endpoint Rays are the sides of the angles The endpoint is the vertex |
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extends forever in one direction and has one endpoint Endpoint is always named first |
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(Can't be defined)
<----------------------> = line |----------------------| = line segment |
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The union of 3 line segments |
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