Geometry: Parallel Lines and Planes Theorems
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- 3-1:If two parallel planes are cut by a third plane,
- then the lines of intersection are parallel.
- 3-2:If two parallel lines are cut by a transversal,
- then alternate interior angles are congruent.
- 3-3:If two parallel lines are cut by a transversal,
- then same-side interior angles are supplementary
- 3-4:If a transversal is perpendicular to one of two parallel lines,
- then it is perpendicular to the other one also.
- 3-5:If two lines are cut by a transversal and alternate interior angles are congruent,
- then the lines are parallel.
- 3-6:If two lines are cut by a transversal and same-side interior angles are supplementary,
- then the lines are parallel.
- 3-7:If two lines in a plane are perpendicular to the same line,
- then the two lines are parallel.
- 3-8:Through a point outside a line,
- there is exactly one line parallel to the given line.
- 3-9:Through a point outside a line,
- there is exactly one line perpendicular to the given line.
- 3-10:If two lines are parallel to a third line,
- then the two lines are parallel to each other.
- 3-11:If the polygon is a triangle,
- then the sum of the measures of the angles is 180.
- 3-11_Corollary 1:If two angles of one triangle are congruent to two angles of another triangle,
- then the third angles are congruent.
- 3-11_Corollary 2:If the triangle is equiangular,
- then each angle has measure 60.
- 3-11_Corollary 3:If the polygon is a triangle,
- then there can be at most one right angle or obtuse angle.
- 3-11_Corollary 4:If the polygon is a right triangle,
- then the acute angles are complementary.
- 3-12:If the polygon is a triangle,
- then the measure of an exterior angle equals the sum of the measures of the two remote interior angles.
- 3-13:If the object is a convex polygon with n sides,
- then the sum of the measures of the angles is (n - 2)180.
- 3-14:If the object is a convex polygon,
- then the sum of the measures of the exterior angles is 360.