Quadrilateral Questions (Yes/No)
Are opposite sides parallel in an isosceles trapezoid?
1 pair (bases)
Are opposite sides congruent in an isosceles trapezoid?
1 pair (legs)
Do diagonals bisect each other in an isosceles trapezoid?
No
Do diagonals bisect opposite angles in an isosceles trapezoid?
No
Are diagonals perpendicular in a rectangle?
No (Unless square)
Are opposite angles congruent in an isosceles trapezoid?
No (lower base angles are congruent to each other upper base angles are conrguent to each other)
Do diagonals bisect opposite angles in a rectangle?
No (only happens when all sides are equal ==> rhombus family only)
Are diagonals perpendicular in an isosceles trapezoid?
No (only perpendicular diagonals are in kite, rhombus and square)
Do diagonals always bisect opposite angles in a parallelogram?
No, unless the parallelogram is a rhombus (all sides need to be congruent for this to happen) (imagine a parallelogram with one pair of parallel sides really long, and other pair of sides really short)
Are consecutive angles supplementary in a parallelogram?
Yes
Are diagonals congruent in an isosceles trapezoid?
Yes
Are diagonals perpendicular in a rhombus?
Yes
Do diagonals bisect opposite angles in a rhombus?
Yes
Given a quadrilateral, if the consecutive angles are supplementary, is it a parallelogram?
Yes
Are the diagonals congruent in a rectangle?
Yes Only rectangle family (including squares) AND isosceles triangles have this.
Are consecutive angles supplementary in a rectangle?
Yes (all parallelograms)
Are opposite angles congruent in a rectangle?
Yes (all parallelograms)
Are opposite angles congruent in a rhombus?
Yes (all parallelograms)
Are opposite sides congruent in a rectangle?
Yes (all parallelograms)
Are opposite sides congruent in a rhombus?
Yes (all parallelograms)
Are opposite sides parallel in a rhombus?
Yes (all parallelograms)
Do diagonals bisect each other in a rectangle?
Yes (all parallelograms)
Do diagonals bisect each other in a rhombus?
Yes (all parallelograms)
Are diagonals perpendicular in a square?
Yes (b/c it's a rhombus)
Are opposite sides parallel in a rectangle?
Yes (because it's a parallelogram)
Are opposite sides parallel in a parallelogram?
Yes (by definition)
Given a quadrilateral, if both pairs of opposite angles are congruent, is it a parallelogram?
Yes (converse of a property)
Given a quadrilateral, if both pairs of opposite sides are congruent, is it a parallelogram?
Yes (converse of a property)
Given a quadrilateral, if the diagonals bisect each other, is it a parallelogram?
Yes (converse of a property)
Are opposite angles congruent in a square?
Yes (it's a parallelogram)
Are opposite sides congruent in a square?
Yes (it's a parallelogram)
Are opposite sides parallel in a square?
Yes (it's a parallelogram)
Do diagonals bisect each other in a square?
Yes (it's a parallelogram)
Are diagonals congruent in a square?
Yes (it's a rectangle)
Do diagonals bisect opposite angles in a square?
Yes (it's a rhombus)
Given a quadrilateral, if one pair of opposite sides is both parallel and congruent, is it a parallelogram?
Yes (neither the reverse of the definition nor the converse of a property)
Are opposite angles congruent in a parallelogram?
Yes (property)
Are opposite sides congruent in a parallelogram?
Yes (property)
Do diagonals bisect each other in a parallelogram?
Yes (property)
Given a quadrilateral, if both pairs of opposite sides are parallel, is it a parallelogram?
Yes (reverse of the definition of parallelogram)
Are consecutive angles supplementary in a rhombus?
Yes (true for all parallelograms)
Are consecutive angles supplementary in a square?
Yes (true for all parallelograms)
Are diagonals always perpendicular in a parallelogram?
no, unless it's a rhombus
Are diagonals congruent in a parallelogram?
no, unless rectangle
Are diagonals congruent in a rhombus?
no, unless square (think of a squished rhombus, two opposite corners get closer as the other pair of corners get further away)