SAT SUBJECT TEST MATH LEVEL 1

PLANE GEOMETRY

CHAPTER 10
Quadrilaterals and Other Polygons

SPECIAL QUADRILATERALS

We will now define five special quadrilaterals and review the important properties of each one.

parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Any side of a parallelogram can be its base, and a line segment drawn from a vertex perpendicular to the opposite base is called the height.

Key Fact I4

Parallelograms have the following properties illustrated in the figures below:

• Opposite sides are parallel:  and .

• Opposite sides are congruent:  and .

• Opposite angles are congruent:  and .

• The sum of the measures of any pair of consecutive angles is 180°. For example, a + b = 180 and b + c = 180.

• A diagonal divides the parallelogram into two congruent triangles: .

• The two diagonals bisect each other: AE = EC and BE = ED.

rectangle is a parallelogram in which all four angles are right angles. Two adjacent sides of a rectangle are usually called the length () and the width (w). Note that the length is not necessarily greater than the width.

Remember

A rectangle is a parallelogram.

Key Fact I5

Since a rectangle is a parallelogram, all of the properties listed in KEY FACT I4 hold for rectangles. In addition:

• The measure of each angle in a rectangle is 90°.

• The diagonals of a rectangle have the same length: AC = BD.

rhombus is a parallelogram in which all four sides have the same length.

Key Fact I6

Since a rhombus is a parallelogram, all of the properties listed in KEY FACT I4 hold for rhombuses. In addition:

• The length of each side of a rhombus is the same.

• The two diagonals of a rhombus are perpendicular.

• The diagonals of a rhombus are angle bisectors.

Remember

A rhombus is a parallelogram.

square is a rectangle in which all four sides have the same length. So a square is both a rectangle and a rhombus.

Key Fact I7

Since a square is a rectangle and a rhombus, all of the properties listed in KEY FACTS I4, I5, and I6 hold for squares.

Remember

A square is a special parallelogram, which is both a rectangle and a rhombus.

trapezoid is a quadrilateral in which exactly one pair of opposite sides is parallel. The parallel sides are called the bases of the trapezoid, and the distance between the two bases is called the height. If the two nonparallel sides are congruent, the trapezoid is called isosceles and, in that case only, the diagonals are congruent.

trapezoid

isosceles trapezoid