Angles of Polygons
Sum of the interior angles of a 17-gon
2700
What theorem states that if a quadrilateral is a parallelogram, then its opposite sides are congruent?
Parallelogram Opposite Sides Theorem
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Parallelogram Opposite Sides Converse
All sides are congruent, but no right angles
Rhombus
True or False: Base angles in trapezoids are always congruent
False. This is only true for isosceles trapezoids.
Sum of the exterior angles of a 23-gon
360
What theorem states that if a quadrilateral is a parallelogram, then its opposite angles are congruent?
Parallelogram Opposite Angles Theorem
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Parallelogram Opposite Angles Converse
4 right angles, but all of the sides are not congruent
Rectangle
A trapezoid is isosceles if and only if its diagonals are what?
The sum of the interior angles of a convex polygon equals 2520 degrees. How many sides does it have?
16
What do the diagonals of a parallelogram do?
Bisect each other
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Parallelogram Diagonals Converse
4 right angles and 4 congruent sides
Square
What is the formula for finding the length of the midsegment of a trapezoid?
(Base 1+Base 2)/2
Each interior angle has a measure of 165 degrees. How many sides?
24
Consecutive angles in a parallelogram add up to what?
180 degrees (supplementary)
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.
Opposite Sides Parallel and Congruent Theorem
If a quadrilateral has right angles and 4 congruent sides, what type(s) of quadrilateral(s) is it?
Rhombus, Rectangle, Square
If a quadrilateral is a kite, then its diagonals are what?
Perpendicular
Each exterior angle has a measure of 6 degrees. How many sides?
60
One angle in a parallelogram is 42 degrees. List the measures of the other three angles.
42, 138, 138
Both pairs of opposite sides are parallel.
Definition of a parallelogram
What is special about the diagonals of a rhombus?
They are perpendicular
If a quadrilateral is a kite, then how many pairs of opposite angles will be congruent?
1