# Chapter 6

## 29 terms · Vocabulary, Theorems and Postulates from Chaper 6

### polygon

a closed plane figure formed by three or more line segments

### convex

A polygon in which all vertices appear to be pushed outward.

### concave

A polygon in which at least one vertex appear to be pushed inward.

### equilateral polygon

a polygon in which all sides are congruent

### equiangular polygon

a polygon whose angles are all congruent

### regular polygon

a polygon that is equilateral and equiangular

### Interior Angles of a Quadrilateral

The sum of the measures of the interior angles of a quadrilateral is 360°.

### List Four Properties of a Parallelogram

1. Opposite sides are congruent
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Diagonals bisect each other

### If one pair of opposite sides of a quadrilateral are ..., then the quadrilateral is a parallelogram.

congruent and parallel

### List at least 4 of the 6 ways to prove quadrilaterals are parallelograms

Show that
1. opposite sides are parallel.
2. opposite sides are congruent.
3. opposite angles are congruent.
4. consecutive angles are supplementary.
5. diagonals bisect each other.
6. one pair of opposite sides are both congruent and parallel.

### rhombus

a parallelogram with 4 congruent sides.

### rectangel

a parallelogram with 4 right angles.

### square

a parallelogram with 4 congruent sides and 4 right angles

### A parallelogram is a rhombus iff its diagonals...

bisect each other.

### A parallelogram is a rhombus iff each diagonal...

bisects the opposite angles.

are congruent

### trapezoid

a quadrilateral withexactly one pair of parallel sides.

### isosceles trapezoid

a trapezoid with congruent legs.

### If a trapezoid is isosceles, the each pair of....

base angles are congruent.

### If a trapezoid has a pair of congruent base angles, then...

it is an isosceles trapezoid.

### A trapezoid is isosceles iff its d...

diagonals are congruent.

### midsegment of a trapezoid

the segment that connects the midpoints of the trapezoids legs.

### Midsegment Theorem for a Trapezoid

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

### If a quadrilateral is a kite, then its d...

diagonals are perpendicular.

### If a quadrilateral is a kite, then exactly one...

pair of opposite angles are congruent.