Idiot\'s Guides Basic Math and Pre-Algebra

170 Part 3: The Shape of the World

CHECK POINT

1. In 'RST, m’R = 48r and m’T = 102r. Find the measure of ’S.


2. In 'RST (described in question 1), side RS is extended through S to point Q to
   create exterior angle ’TSQ. Find the measure of ’TSQ.


3. In 'RST (described in question 1), side RS is extended through S to point Q to
   create exterior angle ’TSQ and through R to point P to create exterior angle
   ’TRP, and side RT is extended through T to point N to form exterior angle
   STN. Find the total of m’TSQ + m’TRP + m’STN.


4. Placidville is 43 miles from Aurora, and Aurora is 37 miles from Lake Grove.
   The distance from Placidville to Lake Grove is at least __ miles but less
   than __ miles.


5. Gretchen lives 5 miles from the library and 2 miles from school. The distance
   from the library to school is between __ miles and __ miles.

Classifying Triangles

Just as trying to talk about all polygons at the same time didn’t make much sense, trying to talk

about all triangles at once can be hard. It’s more practical to break the family of triangles down

into categories, and you usually do that either by the sides or by the angles.

If all the sides of a triangle have different lengths, the triangle is scalene. You can’t say much else

about them, except that all their angles will have different measures, too.

A scalene triangle has three sides of different lengths.

Isosceles triangles are triangles with two congruent sides. The two congruent sides are called the

legs, and the third side is called the base. The angles opposite the congruent sides, often called

the base angles, are congruent to each other. The angle between the legs is usually called the

vertex angle.

a

b a b

c

c