Properties of Parallelograms, Rhombuses, Squares, and Kites
Properties of Parallelograms, Rhombuses, Squares, and Kites is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings, where students learn and apply the defining properties of these special quadrilaterals — such as opposite sides being equal in parallelograms, all sides equal in rhombuses, and perpendicular diagonals in kites — to identify figures and find unknown measurements.
Key Concepts
A parallelogram has opposite sides parallel and congruent, and opposite angles congruent. A rhombus is a parallelogram with four congruent sides. A square is a parallelogram with four congruent sides and four right angles ($90°$). A kite has two pairs of congruent adjacent sides with diagonals perpendicular to each other.
Common Questions
What are the key properties of a parallelogram?
Opposite sides are parallel and congruent, opposite angles are congruent, consecutive angles are supplementary, and diagonals bisect each other.
How is a rhombus different from a parallelogram?
A rhombus is a parallelogram where all four sides are congruent. Its diagonals are perpendicular bisectors of each other and bisect the vertex angles.
What are the unique properties of a kite?
A kite has two pairs of consecutive congruent sides (but opposite sides are not congruent). Its diagonals are perpendicular, and one diagonal bisects the other.
What is Big Ideas Math Advanced 2 Chapter 12 about?
Chapter 12 covers Constructions and Scale Drawings, including properties of special quadrilaterals, angle relationships, geometric constructions, and scale drawings.