## 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.

A ** parallelogram** is a quadrilateral in which both pairs of opposite sides are parallel. Any side of a parallelogram can be its

**, and a line segment drawn from a vertex perpendicular to the opposite base is called the**

*base***.**

*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*.A ** rectangle** is a parallelogram in which all four angles are right angles. Two adjacent sides of a rectangle are usually called the

**() and the**

*length***(**

*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*.A ** 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.

A ** 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.

A ** trapezoid** is a quadrilateral in which exactly one pair of opposite sides is parallel. The parallel sides are called the

**of the trapezoid, and the distance between the two bases is called the**

*bases***. If the two nonparallel sides are congruent, the trapezoid is called**

*height***and, in that case only, the diagonals are congruent.**

*isosceles*trapezoid

isosceles trapezoid