Properties of Shapes Flashcards

Properties of Parallelograms

• Opposite sides are congruent and parallel.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.
• One pair of opposite sides can be both parallel and congruent.

Properties of Rectangles

• All parallelogram properties apply.
• All angles are right angles (90 degrees).
• Diagonals are congruent in length.
• Base angles are congruent.

Properties of Squares

• Includes all properties of parallelograms, rectangles, and rhombuses.
• All sides are congruent and angles are right angles.

Properties of Rhombuses

• All parallelogram properties apply.
• Diagonals are perpendicular to one another.
• Diagonals bisect opposite angles.
• All four sides are congruent.

Properties of Trapezoids

• Has one pair of parallel sides.
• Diagonals create two non-congruent triangles.
• Same side interior angles are supplementary.

Properties of Isosceles Trapezoids

• Diagonals are congruent.
• One pair of opposite sides is congruent.
• Base angles are congruent.

Properties of Kites

• One diagonal bisects the other.
• Diagonals meet at right angles.
• One diagonal creates two non-congruent triangles.
• Two distinct pairs of congruent consecutive sides exist.

Geometric Relationships

• Common properties of parallelogram, rhombus, rectangle, and square include diagonals bisecting each other and congruent opposite angles.
• Rectangles, squares, and isosceles trapezoids share congruent base angles and congruent diagonals.
• Same side interior angles are supplementary across several quadrilaterals, including trapezoids and isosceles trapezoids.

Area Formulas

• Area of a rectangle: ( l \times w )
• Area of a square: ( s^2 ) or ( \frac{1}{2}(d_1 \times d_2) )
• Area of a parallelogram: ( b \times h )
• Area of trapezoid: ( \frac{1}{2}(b_1 + b_2) \times h )
• Area of square, kite, and rhombus: ( \frac{1}{2}(d_1 \times d_2) )

Special Quadrilateral Properties

• In rhombuses and squares, diagonals bisect each other and are perpendicular bisectors.
• Trapezoids have one pair of opposite sides that are parallel, with legs as non-parallel sides.

Formulas Used in Quadrilaterals

• Distance formula proves congruence of opposite sides.
• Slope formula confirms parallel sides.
• Midpoint formula validates that diagonals bisect each other.

Additional Definitions

• Bases refer to the parallel sides in trapezoids and related shapes.
• Legs are the non-parallel sides of trapezoids.