Geometry (H) Chapter 6

diagonal

a segment that connects any two nonconsecutive vertices

Equation to find the Interior sum of a Polygon

(n-2)x180

All exterior angles add up to

360

parallelogram

A quadrilateral with two pairs of parallel sides

What are the 4 properties of a parallelogram

Opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, if one right angle then there are 4 right angles

What are the properties of the diagonals of a parallelogram

They bisect each other; a diagonal separates the parallelogram into 2 congruent triangles

Conditions of a parallelogram

opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, and one pair of opposite sides is parallel and congruent

What is a rectangle

A parallelogram with four right angles

Properties of a rectangle

• all four angles are right angles

• opposite sides are parallel and congruent

• opposite angles are congruent

• Consecutive angles are supplementary

• diagonals bisect each other

The diagonals in a rectangle are…

congruent

rhombus

A parallelogram with four congruent sides

diagonals of a rhombus

are perpendicular, and bisect a pair of opposite angles

square

A parallelogram with four congruent sides and four right angles.

a square is both a…

rectangle and rhombus

conditions for rhombi and squares

If the diagonals of a parallelogram are perpendicular, bisect a pair of opposite angles, and one pair of consecutive sides is congruent

trapezoid

A quadrilateral with exactly one pair of parallel sides

legs

the nonparallel sides of a trapezoid

base angles

formed by the base and one of the legs

isoseles trapezoid

a trapezoid with congruent legs

Properties of Isosceles Trapezoids

Base angles are congruent, one pair of congruent base angles, and diagonals are congruent

midsegment of a trapezoid

the segments that connect the midpoints of the legs of the trapezoid

midsegment of a triangle formula

1/2(x+y)

midsegment can also be called

median

kite

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

properties of a kite

diagonals are perpendicular, and exactly one pair of opposite angles is congruent