# geometry chapter 8

## 22 terms

### Diagonal

segment in a polygon that joins two nonconsecutive vertices

### Polygon Interior Angles Thm.

sum of the interior angles of a convex n-gon is (n-2)180

### Interior angles of a quadrilateral

sum of the angles of a quadrilateral is 360

### Polygon Exterior Angles Thm.

sum of the exterior angles of a convex polygon one angle at each vertex is 360

### Parallelogram

quadrilateral with both pairs of opposite sides parallel

### Properties of Parallelograms

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

### Ways to Prove a Quadrilateral is a Parallelogram

1.Both pairs of opposite sides are parallel
2.Both pairs of opposite sides are congruent
3.Both pairs of opposite angles are congruent
4.Diagonals bisect eachother
5.One pair of opposite sides are congruent and parrallel

### Rhombus

parallelagram with four congruent sides

### Rectangle

parallelagram with four right angles

### Square

parallelagram with four congruent sides and four right angles

### Properties of a Rhombus

1.all the properties of a parallelagram
2.sll sides congruent
3.diagonal bisects opposite congruent angles
4.diagonals perpendicular

### Properties of a Rectangle

1.all properties of a parallelagram
2.four right angles
3.diagonals are congruent

### Properties of a Square

1.All the properties of a parallelagram
2.All the properties of a rhombus
3.All the properties of a rectangle

### Trapezoid

quadrilateral with exactly one pair of parallel sides

### Isosceles Trapezoid

trapezoid with congruent legs

### If a trapezoid is isosceles, then

each pair of base angles is congruent

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

it is an isosceles trapezoid

### A trapezoid is isosceles if and only if

its diagonals are congruent

### Midsegment of a Trapezoid

segment that joins the midpoint of the legs

### Midsegment Thm. for Trapezoids

the midsegment of a trapezoid is
1.parallel to each base
2.half the sum of the bases

### Kite

quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent

### Properties of a Kite

1.diagonals perpendicular
2.one pair of opposite sides congruent