GeoGebra

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Autor:Shaun K
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.

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