Properties and Theorems in .NET

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Properties and Theorems
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The measures of vertical angles are equal. The angles in a linear pair are supplementary. If the angles in a linear pair are equal, the angles are right angles. Angles complementary to the same or to equal angles are equal to each other. Angles supplementary to the same or to equal angles are equal to each other.
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APPENDIX 1 Geometry
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A1.3 Lines
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Two lines in a plane either intersect or are parallel. If two lines intersect, they have exactly one point in common. Two lines in a plane are parallel if they have no common point. When two lines intersect to form equal adjacent angles, the lines are perpendicular. Each of the angles formed by two perpendicular lines is a right angle. The sides of a right angle are perpendicular. A transversal is a line that intersects two or more coplanar lines in distinct points. In Fig. A1.2, lines m and n are cut by transversal t. When two lines are cut by a transversal, the angles formed are classified by their location. The angles between the two lines are called interior angles and the angles not between the two lines are called exterior angles. Interior or exterior angles are said to alternate if the two angles have different vertices and lie on opposite sides of the transversal. A pair of corresponding angles are two angles, one an interior angle and one an exterior angle, that have different vertices and lie on the same side of the transversal. In Fig. A1.2, the interior angles are numbered 3, 4, 5, and 6 while the exterior angles are numbered 1, 2, 7, and 8. The angles numbered 3 and 6 and the angles numbered 4 and 5 are pairs of alternate interior angles. The angles numbered 1 and 8 and those numbered 2 and 7 are pairs of alternate exterior angles. The pairs of corresponding angles are numbered 1 and 5, 2 and 6, 3 and 7, and 4 and 8.
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Fig. A1.2
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Properties and Theorems
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In a plane, if two lines are perpendicular to the same line, then the lines are parallel. Two lines parallel to a third line are parallel to each other. If two parallel lines are cut by a transversal, then the alternate interior angles are equal. If two parallel lines are cut by a transversal, then the alternate exterior angles are equal. If two parallel lines are cut by a transversal, then the corresponding angles are equal. If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary. Any pair of horizontal lines are parallel. Any pair of vertical lines are parallel. Any vertical line is perpendicular to any horizontal line. If two angles have their sides parallel, right side to right side and left side to left side, then the angles are equal. If two angles have their sides perpendicular, right side to right side and left side to left side, then the angles are equal. If two lines are cut by a transversal so that the alternate interior angles formed are equal, then the lines are parallel. If two lines are cut by a transversal so that the alternate exterior angles formed are equal, then the lines are parallel. If two lines are cut by a transversal so that the corresponding angles formed are equal, then the lines are parallel.
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APPENDIX 1
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Geometry
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If two lines are cut by a transversal so that the interior angles on the same side of the transversal are supplementary, then the lines are parallel. If a transversal is perpendicular to one of two parallel lines, it is perpendicular to the other one as well. Through a point not on a line there is exactly one line parallel to a given line. Through a point not on a line there is exactly one line perpendicular to a given line. In a plane, there is exactly one line perpendicular to a given line at any point on the line.
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