(13) BK is the altitude and BD is the base of both rectangle BDJK and triangle CBD.

(14) The area of triangle CBD is one-half the area of rectangle BDJK. Therefore, the areas of

rectangle BDJK and square FBCG are equal.

(15) The area of square ABDE is equal to the sum of the areas of the two rectangles (AKJE

and BDJK). Therefore, the area of square ABDE is also equal to the sum of the two squares (AIHC and

FBCG).

b. A special case of the right triangle, where each side can be divided into an integral number of

basic units, is shown in Figure 3-32. The length of side A is three units, the length of side B is four

units, and the length of the hypotenuse (side C) is five units. This triangle, called a 3-4-5 right triangle,

is often used to mark out long sides with an included right angle. Triangles with sides that are multiples

of 3, 4, and 5 (such as 15, 20, and 25) are also considered to be 3-4-5 right triangles. There are other

right triangles whose sides can be divided into an integral number of basic units, one of which has sides

that are 5, 12, and 13 units long. However, the 3-4-5 triangle is the easiest to remember and the most

commonly used.

Equal triangles are similar, but similar triangles are not necessarily equal. The important relationship of

similar triangles is that a direct proportionality exists between corresponding sides. The following

theorems can be used to determine whether triangles are similar.

a. Theorem 1. A line parallel to one side of a triangle and intersecting the other two sides

divides these two sides proportionally. This condition is shown in Figure 3-33, in which the following

proportion exists:

AD : DC = BE : EC