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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


Sameside 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 sameside interior angles: If two parallel lines are cut by a transversal...

then sameside 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 sameside 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 sameside 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 subtheorem)


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

11gon


A polygon with 12 sides

dodecagon


A polygon with n sides

ngon


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 (n2)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
