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30 Cards in this Set
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parallelogram

a quadrilateral with both pairs of opposite sides parallel


Complete the theorem: If the opposite sides of a quadrilateral are congruent, then...

the quadrilateral is a parallelogram


If opposite angles of a quadrilateral are congruent, then...

the quadrilateral is a parallelogram


If a quadrilateral is a parallelogram then...

the diagonals of the parallelogram bisect each other


If both pairs of opposite sides of a quadrilateral are congruent, then

the quadrilateral is a parallelogram


If one pair of opposite sides of a quadrilateral are both congruent and parallel, then...

the quadrilateral is a parallelogram


If both pairs of opposite angles of a quadrilateral are congruent, then...

the quadrilateral is a parallelogram


If the diagonals of a quadrilateral bisect each other, then...

the quadrilateral is a parallelogram


How do you prove a quadrilateral is a parallelogram?

1. Show that both pairs of opposite sides are parallel
2. Show that both pairs of opposite sides are congruent 3. Show that one pair of opposite sides are both congruent and parallel 4. Show that both pairs of oppoiste angle are congruent 5. Show that the diagonals bisect each other 

If 3 or more parallel lines cut off congruent segments on one transversal, then...

they cut off congruent segments on every transversal


If two lines are parallel,...

then all points on one line are equidistant from the other line


If a line that contains the midpoint of one side of a triangle and is parallel to another side,...

then the line passes through the midpoint of the third side


If a segment joins the midpoints of 2 sides of a triangle,...

then it is parallel to the third side and is half as long as the third side.


Rectangle

A quadrilateral with four right triangles. Therefore, every rectangle is a parallelogram.


Rhombus

A quadrilateral with four congruent sides.Therefore, every rhombus is a parallelogram.


Square

A quadrilateral with four right angles and four congruent sides. Therefore, every square is a rectangle, a rhombus, and a parallelogram.


If a quadrilateral is a rectangle,...

then its diagonals are congruent


If a quadrilateral is a rhombus,...

then its diagonals are perpendicular


If each diagonal of a quadrilateral bisects two angles,...

then the quadrilateral is a rhombus.


If a point is the midpoint of the hypotenuse of a right triangle,...

then it is equidistant from the three vertices.


If an angle of a parallelogram is a right angle,...

then then the parallelogram is a rectangle.


If two consecutive sides of a parallelogram are congruent,...

then the parallelogram is a rhombus.


Trapezoid

A quadrilateral with exactly one pair of parallel sides.


Bases of a trapezoid

the parallel sides.


Legs of a trapezoid

the two sides that are not parallel.


Isosceles Trapezoid

A trapezoid with congruent legs


If a quadrilateral is a trapezoid,...

then the base angles are congruent


Median of a Trapezoid

the segment that joins the midpoints of the legs of the trapezoid.


If a segment is the median of a trapezoid,...

then it is parallel to the bases, and has a length equal to the average of the base lengths.


Properties of a Parallelogram

A. Opposite sides are congruent.
B. Opposite sides are parallel C. Opposite angles are congruent D. Diagonals bisect each other 