legs;the angle formed by these two legs is called the vertex angle;and the baseis the
side opposite the vertex angle. The two angles that are formed by the base and the legs
are called the triangle’s base angles.
How is the Pythagorean Theoremconnected to right triangles?
The Pythagorean Theorem deals with right triangles: Simply stated, the sum of the
squares of the legs equals the square of the hypotenuse (longest side). The converse of
the Pythagorean Theorem is also true: If the sum of the squares of a triangle’s two
sides equals the square of the longest side, then the triangle is a right triangle. (For an
illustration of the Pythagorean Theorem, see “History of Mathematics.”)
What are the various types of quadrilaterals?
There are several types of quadrilaterals, which are polygons with four sides. Interest-
ingly enough, some definitions can be “combined”; for example, if a quadrilateral is
both a rhombus and a rectangle, it is truly a square. The following lists the common
quadrilaterals:
Square—The most obvious quadrilateral is the square. It is an equiangular
quadrilateral with four right angles (it is also defined as having four congruent sides).
Rectangle—The second most well-known quadrilateral is the rectangle, a quadri-
lateral with four right angles, with the opposite sides parallel and congruent, and
opposite angles congruent.
Parallelogram—A parallelogram is a quadrilateral with both pairs of opposite
sides parallel; thus, opposite sides and angles are congruent.
Rhombus—A rhombus is a parallelogram with four equilateral (or congruent) sides.
Trapezoid—A trapezoid is a quadrilateral with exactly one pair of parallel sides.
This is also seen in books as “a quadrilateral with at least one pair of parallel sides,”
but this latter definition is often debated among mathematicians, as the meaning is
not the same as the first statement. With trapezoids, the parallel sides are called the
bases;the nonparallel sides are called the legs.
Isosceles trapezoid—An isosceles trapezoid is one with nonparallel sides that are
equal in length, or a trapezoid with a pair of equiangular base angles. The legs of an
isosceles trapezoid are congruent. (For more about these figures, see elsewhere in this
chapter.)
What is a circle?
A circle is one of the most fundamental shapes in geometry—and one shape we com-
monly see every day. For mathematicians, a circle is defined as a set of points on a
plane at a certain distance from a center point. In reality, a circle is a polygon with an
infinite number of sides. 183