Best notes
A square is a parallelogram. A kite is a parallelogram. A trapezoid has congruent legs. A square is both a rectangle and a rhombus. A rectangle is a rhombus. A trapezoid is a quadrilateral.
Properties of Parallelograms
- The opposite angles of a parallelogram are congruent.
- The consecutive angles of a parallelogram are supplementary.
- The opposite sides of a parallelogram are congruent.
- The diagonals of a parallelogram bisect each other.
Properties of Other Quadrilaterals
- The diagonals of an isosceles trapezoid are congruent.
- The diagonals of a kite are perpendicular.
Given: Parallelogram ABCD
Prove: ∠A≅∠C , ∠B≅∠D .
Proof:
By the definition of a parallelogram, AD¯¯¯¯¯∥CB¯¯¯¯¯ and AB¯¯¯¯¯∥CD¯¯¯¯¯ . ∠A and ∠B are consecutive angles of parallel lines, so they are supplementary. Also, ∠B and ∠C are consecutive angles of parallel lines, so they are supplementary. By the congruent supplements theorem, ∠A≅∠C . ∠C and ∠D are also consecutive angles of parallel lines, so they are supplementary. So by the congruent supplements theorem, ∠B≅∠D .
The diagram shows the relationship among quadrilaterals.
