Geometry Chapter 5 Vocab

convex poygon

a polygon in which each interior angle has a measure less than 180^o

diagonals of a polygon

any segment that connects two nonconsecutive vertices

Parallelogram

both pairs of opposite sides are parallel

Rectangle

a parallelogram in which at least one angle is a right angle

rhombus

a parallelogram in which at least 2 consecutive sides are congruent

square

a parallelogram that is both a rectangle and a rhombus

kite

a quadrilateral in which 2 disjoint pairs of consecutive sides are congruent

trapezoid

a quadrilateral with exactly one pair of parallel sides

isosceles trapezoid

a trapezoid in which the nonparallel sides (legs) are congruent

properties of parallelograms

• opposite sides are parallel

• opposite sides are congruent

• opposite angles are congruent

• diagonals bisect each other

• consecutive angels are supplementary

properties of rectangles

• all properties of a parallelogram

• all angles are right angles

• diagonals are congruent

properties of kits

• two disjoint pairs of consecutive sides are congruent

• diagonals are perpendicular

• one diagonal is the perpendicular bisector of the other

• one of the diagonals bisects a pair of opposite angles

• one pair of opposite angles are congruent

properties of rhombuses

• all properties of a parallelogram

• all properties of kites

• all sides are congruent (equilateral)

• diagonals bisect the angles

• diagonals are perpendicular bisectors of each other

• diagonals form 4 right triangles

properties of squares

• all properties of rectangles

• all properties of rhombuses

• diagonals form 4 isosceles right triangles

properties of isosceles trapezoids

• legs are congruent

• bases are parallel

• lower base angles are congruent

• upper base angles are congruent

• diagonals are congruent

• any lower base angle is supplementary to an upper base angle

to prove a quadrilateral is a parallelogram

• has both pairs of opposite sides congruent

• has both pairs of opposite sides parallel

• one pair of opposite sides are both parallel and congruent

• has diagonals that bisect each other

• has both pairs of opposite angles congruent

proving that a quadrilateral is a rectangle

1). show that it is a parallelogram AND it had at least one right angle

2). show that is is a parallelogram AND its diagonals are congruent

3). Show that all four angles are right angles

proving that a quadilateral is a kite

1). show that 2 disjoint pairs of consecutive sides are congruent

2.) show that one of the diagonals perpendicular bisects the other diagonal

proving that a quadrilateral is a square

1.) show that a quadrilateral is both a rectangle and a rhombus

proving that a quadrilateral is a rhombus

1.) show that a quadrilateral is a parallelogram AND show it contains a pair consecutive congruent sides

2.) show that a quadrilateral is a parallelogram AND either of the diagonals bisect the 2 angles

3.) show that the diagonals are perpendicular bisectors of each other

proving that a trapezoid is an Isosceles trapezoid

1.) show that the non-parallel sides (legs) of a trapezoid are congruent

2.) show that the lower OR upper base angles of the trapezoid are congruent

3.) show that the diagonals of the trapezoid are congruent