Math-Book-GMAT-Club

• The diagonals of a parallelogram bisect each other.
• Consecutive angles are supplementary, add to 180°.
• The area, , of a parallelogram is , where is the base of the parallelogram and is its height.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some other
quadrilaterals, which are obtained by adding restrictions of various kinds:
• A rectangle is a parallelogram but with all angles fixed at 90°
• A rhombus is a parallelogram but with all sides equal in length
• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°
Rectangle A 4‐sided polygon where all interior angles are 90°
Properties and Tips
• Opposite sides are parallel and congruent
• The diagonals bisect each other
• The diagonals are congruent
• A square is a special case of a rectangle where all four sides are the same length.
• It is also a special case of a parallelogram but with extra limitation that the angles are fixed at 90°.
• The two diagonals are congruent (same length).
• Each diagonal bisects the other. In other words, the point where the diagonals intersect (cross), divides
each diagonal into two equal parts.
• Each diagonal divides the rectangle into two congruent right triangles. Because the triangles are congruent,
they have the same area, and each triangle has half the area of the rectangle.
• where: is the width of the rectangle, h is the height of the rectangle.
• The area of a rectangle is given by the formula .
A rectangle can be thought about in other ways:
• A square is a special case of a rectangle where all four sides are the same length. Adjust the rectangle above to
create a square.
• It is also a special case of a parallelogram but with extra limitation that the angles are fixed at 90°.
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GMAT Club Math Book
part of GMAT ToolKit iPhone App