geometry unit 5

Parallelogram

A quadrilateral whose opposite sides are parallel

Parallelogram opposite angles conjecture

The opposite angles of a parallelogram are congruent

Parallelogram consecutive angles conjecture

The consecutive angles of a parallelogram are supplementary

Parallelogram opposite sides conjecture

The opposite side of a parallelogram are congruent

Parallelogram diagonals conjecture

The diagnosis of a parallelogram bisect each other

Rhombus

A parallelogram with four congruent sides, or an equilateral parallelogram. Can be constructed with a double edge straight edge.

Rhombus diagonal conjecture

The diagonals of a rhombus are perpendicular and they bisect each other.

Rhombus angles conjecture

The diagonals of a rhombus bisect the angles of the rhombus

Rectangle

A parallelogram with four congruent angles, or an equiangular parallelogram

Rectangle diagonals conjecture

The diagonals of a rectangle are congruent and bisect each other

Square

A special rhombus (an equiangular rhombus) and a special rectangle (an equilateral)

Shared square properties

A square has the diagonal properties of a parallelogram, a rhombus, and a rectangle

Square diagonals conjecture

The diagonals of a square are perpendicular, congruent, and bisect each other

Three midsegment conjecture

The three mindsegments of a triangle divide it into 4 congruent triangles

Triangle midsegment conjecture

A midsegment of a triangle is parallel to the third side and half the length of the third side.

Trapezoid midsegment conjecture

The midsegment of a trapezoid is parallel to the base and equal in length to the average of the base lengths.