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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