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27 Cards in this Set
- Front
- Back
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Postulate 1: Ruler Postulate
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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. (p. 12)
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Postulate 2: Segment Addition Postulate
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If B is between A and C, then AB + BC = AC. (p. 12)
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Postulate 3: Protractor Postulate
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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 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 with 180. b. If ray OP is paired with x, and ray OQ with y, then m<POQ = Ix - yI. (p. 18) |
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Postulate 4: Angle Addition Postulate
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If point B lies in the interior of <AOC, then m<AOB + m<BOC = m<AOC. If <AOC is a straight angle and B is any point not on line AC, then m<AOB + m<BOC = 180. (p. 18)
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Postulate 5: Points and Dimension
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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. (p. 23)
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Postulate 6: Line
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Through any two points there is exactly one line. (p. 23)
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Postulate 7: Plane
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Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. (p. 23)
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Postulate 8: Points & Plane
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If two points are in a plane, then the line that contains the points is in that plane. (p. 23)
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Postulate 9: Two Intersecting Planes
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If two planes intersect, then their intersection is a line. (p. 23)
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Postulate 10: Lines Cut by a Transversal #1
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If two parallel lines are cut by a transversal, then corresponding angles are congruent. (p. 78)
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Postulate 11: Lines cut by a Transversal #2
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If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. (p. 83)
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Postulate 12: SSS Postulate
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If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. (p. 122)
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Postulate 13: SAS Postulate
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If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. (p. 122)
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Postulate 14: ASA Postulate
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If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. (p. 123)
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Postulate 15: AA Similarity Postulate
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If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. (p. 255)
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Postulate 16: Arc Addition Postulate
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The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs. (p. 339)
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Postulate 17: Square Area
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The area of a square is the square of the length of a side (A = s^2) (p. 423)
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Postulate 18: Area Congruence Postulate
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If two figures are congruent, then the have the same area. (p. 423)
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Postulate 19: Area Addition Postulate
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The area of a region is the sum of the areas of its non-overlapping parts. (p. 424)
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Convex Polygon
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A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
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Theorem 3 - 13: Angles of a Polygon #1
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The sum of the measures of the angles of a convex polygon with N sides is (N - 2)180.
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Theorem 3 - 14: Angles of a Polygon #2
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The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
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Theorem 4 - 4: HL Theorem
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If the hypotenus and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. (p. 141)
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Theorem 5 - 6: Parallelogram #3
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If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. (p. 172)
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Theorem 5 - 7: Parallelogram #4
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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (p. 172)
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Theorem 5 - 5: Parallelogram #1
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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. (p. 173)
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Theorem 5 - 6: Parallelogram #2
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If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram (p. 172)
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