Geometry - Quadrilaterals (Parallelograms, Kites, and Trapezoids)

Kite

Exactly 2 pairs of consecutive congruent sides

1 pair f opposite angles are congruent

Diagonals are perpendicular

Trapezoid

1 pair of opposite sides (bases) are parallel

Consecutive angles are supplementary

Midsegment of a Trapezoid

Line that connects the midpoints of the legs, equal to the average of the two bases of a trapezoid

Isosceles Trapezoid

Non parallel sides (legs) are congruent

Diagonals are congruent

Base angles are congruent

Opposite angles are supplementary

Type of Trapezoid

Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals bisect each other

Rhombus

Four congruent sides

Diagonals are perpendicular

Diagonals bisect opposite angles

Type of parallelogram

Rectangle

Four right angles

Diagonals are congruent

Type of parallelogram

Square

Four congruent sides

Four right angles

All the properties of rectangles, rhombi, and parellelograms

to prove rectangles

Prove it’s a parallelogram with congruent diagonals

Prove it’s a parallelogram with one right angle

Prove that ALL angles are right angles

to prove rhombi

Prove that it's a parallelogram with perpendicular diagonals

Prove that it’s a parallelogram with diagonals that bisect the angles

Prove that all sides are congruent

to prove a square

Prove it’s a rectangle with 4 congruent sides

Prove that it’s a rhombus with 4 right angles

Prove it’s a quadrilateral with 4 congruent sides AND 4 congruent angles

to prove a trapezoid

Prove it’s a quadrilateral with EXACTLY 1 pair of parallel sides

to prove an isosceles trapezoid

Prove it’s a trapezoid with congruent legs

Prove it’s a trapezoid with a pair of congruent base angles (either upper or lower)

Prove it’s a trapezoid with congruent base angles

Properties of midsegment

Connects the midpoints of the legs of a trapezoid

Parallel to the bases of a trapezoid

Length is equal to half the sum of the bases