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| Theorems to prove parallel lines are congruent |
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Definition
Theorem 30: The measure of a triangle is greater than the measure of either remote interior angle
Theorem 31: if 2 alternate interior angles are congruent the lines are parallel
Theorem 32: If 2 alternate exterior angles are congruent the lines are parallel
Theorem 33: If 2 corresponding angles are congruent, the lines are parallel
Theorem 34: If 2 lines are cut by a transversal such that 2 interior angles on the same side of the transversal are supplementary, the lines are parallel
Theorem 35: If 2 lines are cut by a transversal such that 2 exterior angles on the same side of the transversal are supplementary, the lines are parallel
Theorem 36: If 2 coplanar lines are perpindicular to a 3rd line, they are parallel |
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| Through a point not on a line there is exactly one parallel to the given line |
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Theorem 37: If parallel lines, alternate interior angles are congruent
Theorem 38: If 2 parallel lines are cut by a transversal, then any pair of the angles formed are either congruent or supplementary |
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| Six theorems about parallel lines |
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Definition
Theorem 39: if parallel lines, alternate exterior angles are congruent
Theorem 40: if parallel lines, corresponding angles are congruent
Theorem 41: If 2 parallel lines are cut by a transversal, each apir of interior angles on the same side of the transversal are supplementary
Theorem 42: if 2 parallel lines are cut by a transversal, each pair of exterior angles on the same side of the transversal are supplementary
Theorem 43: in a plane, if a line is perpindicular to 1 of 2 lines, it is perpindicular to the other
Theorem 44: if 2 lines are parallel to a 3rd line, they are parallel to each other (transitive property of parallel lines) |
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| a polygon in which each interior angles measures less than 180 |
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| segment that connects 2 nonconsecutive (nonadjacent) vertices of the polygon |
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| quadrilateral in which both pairs of opposite sides are parallel |
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| a parallelogram in which at least 1 angle is right |
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| a parallelogram in which at least 2 consecutive aides are congruent |
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| quadrilateral where 2 disjoint pairs of consecutive sides are congruent |
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| parallelogram that is both a rectangle and a rhombus |
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| quadrilateral w/ exactly 1 pair of parallel sides called bases |
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| a trapezoid in which 2 nonparallel sides (legs) are congruent |
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