Chapter 7: Quadrilaterals and Other Polygons

Angles of Polygons

100

Sum of the interior angles of a 17-gon

2700

200

Sum of the exterior angles of a 23-gon

360

300

The sum of the interior angles of a convex polygon equals 2520 degrees. How many sides does it have?

16

400

Each interior angle has a measure of 165 degrees. How many sides?

24

500

Each exterior angle has a measure of 6 degrees. How many sides?

60

Properties of Parallelograms

100

What theorem states that if a quadrilateral is a parallelogram, then its opposite sides are congruent?

Parallelogram Opposite Sides Theorem

200

What theorem states that if a quadrilateral is a parallelogram, then its opposite angles are congruent?

Parallelogram Opposite Angles Theorem

300

What do the diagonals of a parallelogram do?

Bisect each other

400

Consecutive angles in a parallelogram add up to what?

180 degrees (supplementary)

500

One angle in a parallelogram is 42 degrees. List the measures of the other three angles.

42, 138, 138

Quadrilateral is a Parallelogram

100

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Parallelogram Opposite Sides Converse

200

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

Parallelogram Opposite Angles Converse

300

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

Parallelogram Diagonals Converse

400

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

500

Both pairs of opposite sides are parallel.

Definition of a parallelogram

Special Parallelograms

100

All sides are congruent, but no right angles

Rhombus

200

4 right angles, but all of the sides are not congruent

Rectangle

300

4 right angles and 4 congruent sides

Square

400

If a quadrilateral has right angles and 4 congruent sides, what type(s) of quadrilateral(s) is it?

Rhombus, Rectangle, Square

500

What is special about the diagonals of a rhombus?

They are perpendicular

Trapezoids and Kites

100

True or False: Base angles in trapezoids are always congruent

False. This is only true for isosceles trapezoids.

200

A trapezoid is isosceles if and only if its diagonals are what?

Congruent

300

What is the formula for finding the length of the midsegment of a trapezoid?

(Base 1+Base 2)/2

400

If a quadrilateral is a kite, then its diagonals are what?

Perpendicular

500

If a quadrilateral is a kite, then how many pairs of opposite angles will be congruent?

1