Geometry-Classe Memory Work Chapters 1-3
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38 terms
Terms | Definitions |
|---|---|
 Segment Addition Postulate | If B is between A and C, then AB + BC = AC. |
| Angle Addition Postulate | If point B lies in the interior of angle AOC, then the measure of angle AOB + the measure of angle BOC = the measure of angle AOC. If angle AOC is a straight angle and B is any point not on ray AC, then the measures of AOB + the measure of BOC = 180. |
| Postulate 5 | A line that contains at least 2 points; a plane contains at least 3 points not all in 1 line; space contains at least 4 points not all in 1 plane. |
| Postulate 6 | Through any 2 points there is exactly 1 line. |
| Postulate 7 | Through any points there is at least 1 plane, and through any 3 noncollinear points there is exactly 1 plane. |
| Postulate 8 | If 2 points are in a plane, then the line that contains the points is in that plane. |
| Postulate 9 | If 2 planes intersect, then their intersection is a line. |
| Postulate 10 | If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. |
| Postulate 11 | If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent, then the lines are parallel. |
| 1-1 | If 2 lines intersect, then they intersect in exactly 1 point. |
| 1-2 | Through a line and a point not in the line there is exactly 1 plane. |
| 1-3 | If 2 lines intersect, then exactly one plane contains the lines. |
| Midpoint Theorem | If M is the midpoint of line segment AB, then AM = 1/2 of AB and MB = 1/2 of AB. |
| Angle Bisector Theorem | If ray BX is the bisector of angle ABC, then the measure of angle ABX = 1/2 the measure of angle ABC and measure XBC = 1/2 the measure of angle ABC. |
| 2-3 | Vertical angles are congruent. |
| 2-4 | If 2 lines are perpendicular, then they form congruent adjacent angles. |
| 2-5 | If 2 lines form congruent adjacent angles, then the lines are perpendicular. |
| 2-6 | If the exterior sides of 2 adjacent acute angles are perpendicular, then the angles are complementary. |
| 2-7 | If 2 angles are supplements of congruent angles (or of the same angle), then the 2 angles are congruent. |
| 2-8 | If 2 angles are complements of congruent angles (or of the same angle), then the 2 angles are congruent. |
| 3-1 | If 2 parallel planes are cut by a 3 plane, then the lines of intersection are parallel. |
| 3-2 | If 2 parallel lines are cut by a transversal, then alt. int. angles are congruent. |
| 3-3 | If 2 parallel lines are cut by a transversal, then same-side int. angles are supplementary. |
| 3-4 | If a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other 1 also. |
| 3-5 | If 2 lines are cut by a transversal and alt. int .angles are congruent, then the lines are parallel. |
| 3-6 | If 2 lines are cut by a transversal and same-side int. angles are supp., then the lines are parallel. |
| 3-7 | In a plane 2 lines perpendicular to the same line are parallel. |
| 3-8 | Through a point outside a line, there is exactly 1 line parallel to the given line. |
| 3-9 | Through a point outside a line, there is exactly 1 line perpendicular to the given line. |
| 3-10 | 2 lines parallel to a 3rd line are parallel to each other. |
| 3-11 | The sum of the measures of the angles of a triangle is 180. |
| Corollary 1 (3-11) | If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent. |
| Corollary 2 (3-11) | Each angle of an equiangular triangle has measure 60. |
| Corollary 3 (3-11) | In a triangle, there can be at most 1 right angle or obtuse angle. |
| Corollary 4 (3-11) | The acute angles of a right angle are complementary. |
| 3-12 | The measure of an exterior angle of a triangle equals the sum of the measures of the 2 remote int. angles. |
| 3-13 | The sum of the measures of the angles of a convex polygon with (n) sides is (n - 2)180. |
| 3-14 | The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360. |
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