501 Geometry Questions

3. Right triangleshave one right angle that measures 90° and two acute
   angles. In right triangles, the right angle is always opposite the longest
   side of the triangle, which is called the hypotenuse. The other two sides,
   which are the sides of the right angle, are called the legs. (Remember, it
   is impossible for a triangle to have two right angles because the sum of
   the interior angles of a triangle always equals 180°.) The following
   ΔTOS is a right triangle.

● Right Triangle TOS

● m∠TSO = 90°

● m∠TOS and m∠STO < 90°

We’ve just looked at how to classify triangles by the congruence of their
sides and by the size of their angles. Lastly, let’s focus on how to classify tri-
angles by the congruence of their angles. Luckily, you already had a preview
of this in the beginning of this chapter!

1. Scalene triangleshave no congruent angles (and no
   congruent sides).


2. Isosceles triangleshave two congruent angles (and two
   congruent sides).


3. Equilateral triangleshave three congruent angles (and
   three congruent sides). The three congruent angles always
   each equal 60°.

One thing to keep in mind is that acute, obtuse, and right triangles can
also be classified as scalene, isosceles, or equilateral. For example, ΔORQ
in the following figure is both an isosceles triangle and a right triangle: it
has a vertex that is 90° and two congruent base angles that are each 45°.

T

S O

leg

leg

50 ° hypotenuse

40 °

501 Geometry Questions