Quadrilaterals Flashcards
What are the properties of all parallelograms?
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, a diagonal forms two congruent triangles, diagonals bisect each other
Definition of parallelogram
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel
What are the properties of all rectangles?
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, a diagonal forms two congruent triangles, diagonals bisect each other, diagonals are congruent, all angles are right angles
What are the properties of all rhombi?
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, a diagonal forms two congruent triangles, diagonals bisect each other, diagonals are perpendicular, a diagonal bisects two angles, all sides are congruent
What are the properties of all squares?
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, a diagonal forms two congruent triangles, diagonals bisect each other, diagonals are congruent, diagonals are perpendicular, a diagonal bisects two angles, all angles are right angles, all sides are congruent
How can you solve for a parallelogram?
Solve for:
Both pairs of opposite to be parallel, both pairs of opposite sides to be congruent, one pair of opposite sides to be both parallel and congruent, diagonals that bisect each other, both pairs of opposite angles are congruent, an angle that is supplementary to BOTH of its consecutive angles
What is a trapezoid?
A quadrilateral that has at least one pair of opposite sides parallel
What is an isosceles trapezoid?
A trapezoid with congruent base angles
What is a rhombus?
A parallelogram with two consecutive sides congruent
What is a rectangle?
A parallelogram with at least one right angle
What is a square?
A rectangle with two consecutive sides congruent
How can you prove a quadrilateral is a rectangle?
Solve for:
If it’s a parallelogram with one right angle, if it’s equiangular, if it’s a parallelogram whose diagonals are congruent
How can you prove a quadrilateral is a rhombus?
Solve for:
A parallelogram with two congruent consecutive sides, if it’s equilateral, if it’s a parallelogram whose diagonals are perpendicular to each other, if it’s a parallelogram and one diagonal bisects both angles to which it is drawn
How can you prove a quadrilateral is a square?
Solve for:
The shape is a rhombus and the shape is a rectangle
(If a quadrilateral is both a rhombus and a rectangle then it is a square)
How can you prove that a quadrilateral is an isosceles trapezoid?
Solve for:
A trapezoid that has congruent base angles, a trapezoid with congruent diagonals, a trapezoid with a pair of opposite angles that are supplementary
