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### 58 Cards in this Set

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 Parallel lines Coplanar lines that do not intersect Skew Lines noncoplanar lines, they are not parallel and do not intersect Parallel Planes planes that do not intersect Parallel line and plane A line and a plane that do not intersect. Complete the theorem about parallel planes: If two parallel planes are cut by a third plane... then the lines of intersection are parallel Transversal A line that intersects two or more coplanar lines in different points Alternate Interior Angles two nonadjacent interior angles on opposite sides of the transversal Corresponding Angles(<->) two angles in corresponding positions relative to the two lines Same-side interior angles two interior angles on the same side of the transversal. Complete the postulate: If two parallel lines are cut by a transversal... then corresponding angles are congruent. Complete the theorem: If two parallel lines are cut by a transversal... then alternate interior angles are congruent. Complete the theorem about same-side interior angles: If two parallel lines are cut by a transversal... then same-side interior angles are supplementary Complete the theorem: If a transversal is perpendicular to one of two prallel lines... then it is perpendicular to the other one also Complete the postulate: If two lines are cut by a transversal and corresponding angles are congruent... then the lines are parallel Complete the theorem: If two lines are cut by a transversal and alternate interior angles are congruent... then the lines are parallel Complete the theorem: If two lines are cut by a transversal and same-side interior angles are supplementary... then the lines are parallel Complete the theorem: If two lines are in a plane and perpendicular to the same line... then the lines are parallel Complete the theorem: If a point is not on a line... then there is exactly one line through the point parallel to the given line Complete the theorem: If a point is not on a line... then there is exactly one line that passes through the point that is perpendicular to the given line Complete the theorem: If two lines are parallel to a third line... then they are parallel to each other How can you prove two lines are parallel? 1. Show that a pair of corresponding angles are congruent. 2. Show that a pair of alternate interior angles are congruent. 3. Show that a pair of same-side interior angles are supplementary. 4. In a plane show that both lines are perpendicular to a third line. 5. Show that both lines are parallel to a third line. Triangle, Vertex, sides The figure formed by three segments joining three noncollinear points. Each of the points is called a vertex (plural vertices), the segments are called sides. Scalene triangle A triangle with no congruent sides. Equilateral triangle All sides are congruent Isosceles triangle a triangle with at least two congruent sides. Acute triangle Three acute angles Obtuse triangle one obtuse angle Right triangle one right angle Equiangular triangle all angles are congruent Auxillary line a line, ray or segment added to a diagram to help in a proof; it can only meet one condition Complete the theorem: The sum of the measures of.... the angles of a triangle is 180 Corollary A statement that can be proved by applying a theorem ( a sub-theorem) Complete the Corollary: If two angles of one triangle are congruent to two angles of... another triangle, then the third angles are congruent. Complete the Corollary: If two angles of one triangle are congruent to two angles of... another triangle, then the third angles are congruent. Complete the corollary: If a triangle is equiangular... then the measure of each angle is 60 Complete the corollary: If a figure is a triangle... then there is at most one right angle or obtuse angle Complete the corollary: If a triangle is a right triangle... then the acute angles of the triangle are complementary Exterior angle the angle formed when one side of a triangle is extended Remote interior angles the two interior angles opposite an exterior angle of a triangle Complete the theorem: If a triangle has an exterior angle... then the measure of the exterior angle is equal to the sum of the measures of the remote interior angles Polygon A plane figure formed by coplanar segments (sides) such that 1. each segment intersacts exactly two other segments, one at each endpoint 2. no two segment with a common endpoint are collinear Convex Polygon a polygon such that no line containging a side of the polygon contains a point in the interior of the polygon. A polygon with three sides a triangle A polygon with four sides quadrilateral A polygon with five sides pentagon A polygon with six sides hexagon A polygon with seven sides heptagon A polygon with eight sides octagon A polygon with nine sides nonagon A polygon with ten sides decagon A polygon with 11 sides 11-gon A polygon with 12 sides dodecagon A polygon with n sides n-gon Diagonal a segment joining two nonconsecutive vertices Complete the theorem: If a convex polygon has n sides... then the sum of the measures of the angles is (n-2)180 Complete the theorem: If a convex polygon has one exterior angle at each vertex... then the sum of the measures of the exterior angles is 360 Regular Polygon a polygon that is both equilateral and equiangular Inductive reasoning A type of reasoning in which the conclusion is based on several past observations