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24 Cards in this Set
- Front
- Back
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Postulate 7: The Parallel Postulate
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Through a point not on a line, there is exactly one line line parallel to the line.
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Theorem 16
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In a plane, two points each equidistant from the endpoints of a line segment determine the perpendicular bisector of the line segment.
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Theorem 17
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Equal corresponding angles mean that lines are parallel.
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Theorem 17: Corollary 1
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Equal alternate interior angles mean that lines are parallel.
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Theorem 17: Corollary 2
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Supplementary interior angles on the same side of a transversal mean that lines are parallel.
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Theorem 17: Corollary 3
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In a plane, two lines perpendicular to a third line are parallel.
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Theorem 18
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In a plane, two lines parallel to a third line are parallel to each other.
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Theorem 19
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Parallel lines form equal corresponding angles.
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Theorem 19: Corollary 1
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Parallel lines form equal alternate interior angles.
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Theorem 19: Corollary 2
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Parallel lines form supplementary interior angles on the same side of a transversal.
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Theorem 19: Corollary 3
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In a plane, a line perpendicular to one of two parallel lines is also perpendicular to the other.
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Theorem 20: The Angle Sum Theorem
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The sum of the angles of a triangle is 180 degrees.
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Theorem 20: Corollary 1
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If two angles of one triangle are equal to two angles of another triangle, the third angles are equal.
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Theorem 20: Corollary 2
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The acute angles of a right triangle are complementary.
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Theorem 20: Corollary 3
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Each angles of an equilateral triangle is 60 degrees.
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Theorem 21
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An exterior angle of a triangle is equal to the sum of the remote interior angles.
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Theorem 22: The AAS Theorem
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If two angles and the side opposite one of them in one triangle are equal to the corresponding parts of another triangles, the triangles are congruent.
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Theorem 23: The HL Theorem
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If the hypotenuse and a leg of one right triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
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Construction 6
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To construct a line perpendicular to a given line through a given point.
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Construction 7
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To construct a line parallel to a given line through a given point.
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Angles formed by a transversal
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When a transversal intersects to lines that lie in the same plane, it forms pairs of angles that are given special names.
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Line symmetry
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Two points are symmetric with respect to a line iff the line is the perpendicular bisector of the line segment connecting the two points.
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Parallel lines
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Two lines are parallel iff they lie in the same plane and do not intersect.
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Transversals
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A transversal is a line that "goes across"-that is, "intersects" two or more lines in different points.
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