Chapter 7 Big ideas math geometry

Diagonal

a segment that connects any two nonconsecutive vertices

Polygon Interior Angles Theorem

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

Corollary to the Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a quadrilateral is 360 degrees

equilateral polygon

a polygon with all sides congruent

equiangular polygon

a polygon in which all angles are congruent

regular polygon

a convex polygon that is both equilateral and equiangular

Polygon exterior angles theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

Parallelogram opposite sides theorem

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Parallelogram opposite angles theorem

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Parallelogram Consecutive Angles Theorem

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Parallelogram Diagonals Theorem

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

Parallelogram opposite sides converse

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

Parallelogram opposite angles converse

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

Opposite sides parallel and congruent theorem

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.

Parallelogram diagonals converse

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

quadrilateral

a four-sided polygon

Pentagon

5 sided polygon

Hexagon

6 sides

heptagon/septagon

a polygon with 7 sides

Octagon

a polygon with 8 sides

nonagon

polygon with 9 sides

decagon

a polygon with 10 sides

Hendecagon

11 sided polygon

Dodecagon

12 sided polygon

Rhombus

A parallelogram with four congruent sides

rectangle

A parallelogram with four right angles

Square

A parallelogram with four congruent sides and four right angles.

Rhombus Corollary

A quadrilateral is a rhombus if and only if it has four congruent sides

Rectangle Corollary

A quadrilateral is a rectangle if and only if it has four right angles

Square Corollary

A quadrilateral is a square if and only if it is a rhombus and a rectangle.

Rhombus Diagonals Theorem

A parallelogram is a rhombus if and only if its diagonals are perpendicular

Rhombus Opposite Angles Theorem

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Rectangle Diagonals Theorem

A parallelogram is a rectangle if and only if its diagonals are congruent.

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Isosceles trapezoid

a trapezoid in which the legs are congruent

Isosceles trapezoid base angles theorem

If a trapezoid is isosceles, then each pair of base angles is congruent

Isosceles trapezoid base angles converse

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Isosceles trapezoid diagonals theorem

A trapezoid is isosceles if and only if its diagonals are congruent.

midsegment of a trapezoid

a segment that connects the midpoints of the legs of a trapezoid

Trapezoid Midsegment Theorem

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

Kite

a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

Kite Diagonals Theorem

If a quadrilateral is a kite, then its diagonals are perpendicular.

Kite Opposite Angles Theorem

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.