Diagonals
They are perpendicular
What is the definition of a parallelogram?
A quad. with both opposite sides parallel
What do the consecutive angles of a parallelogram add up to?
180 degrees
What is the formula for the measure of one exterior angle of an n-gon?
360/n
What is the length of the midsegment of a trapezoid?
The average of the two bases.
What is true about the diagonals of any parallelogram?
They bisect each other.
What shape has one pair of parallel sides?
trapezoid
What is the sum of the interior angles of a quad?
360 degrees
What is the formula for the sum of the interior angles of a polygon?
(n-2)180
What theorem states that a quad is a parallelogram if its opposite sides are congruent?
Parallelogram Opposite Sides Converse
What is true about the diagonals of a rhombus
They are perpendicular.
What is name of the two non-parallel sides of a trapezoid?
legs
What is the sum of the exterior angles of a dodecagon?
360 degrees
What is the formula for the measure of one interior angle of a regular polygon?
((n-2)180)/n
What does the kite opposite angles theorem state?
If a quad is a kite, then exactly one pair of opposite angles are congruent.
What is true about the diagonals of a rectangle?
They are congruent.
rhombus and square
If one angle in an isosceles trapezoid measures 130 degrees, what are possible measures of the angle next to it?
130 or 50 degrees
How would you prove that a given parallelogram is a square using its diagonals?
use the slope formula to find if the diagonals are perpendicular and use the distance formula to find if the diagonals are congruent
What does the rhombus opposite angles theorem state?
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
What parallelogram has diagonals that are both perpendicular and congruent?
a square
What parallelogram has 4 right angles?
rectangle and square
What is the measure of one interior angle in a regular 20-gon?
162 degrees
How would you prove that a given quadrilateral is an isosceles trapezoid
Find if only one pair of opposite sides are parallel (same slopes) and if the legs are congruent (same distance)
What does the OSPACT state?
A quad is a parallelogram if one pair of opposite sides are both parallel and congruent.