Name:___________________________
Introduction to Triangles
Date:_____ Period:____
Ms. Anderle
Introduction to Triangles:
The sum of the measures of all of the angles in a triangle is __________.
Triangles can be named by both their angles and their sides. In addition, a triangle
can be named by using both their sides and angles.

Naming Triangles By Angles:
o Acute: ______________________________________________
____________________________________________________
o Right: _______________________________________________
____________________________________________________
o Obtuse: _____________________________________________
____________________________________________________
o Equiangular:___________________________________________
____________________________________________________

Naming Triangles By Sides:
o Scalene:______________________________________________
____________________________________________________
o Isosceles: ____________________________________________
____________________________________________________
o Equilateral:___________________________________________
____________________________________________________
Knowing what type of triangle we have can help to answer a number of triangle
word problems that are given on both the Regents and final exam.
Example 1:
The measure of the vertex angle of an isosceles triangle exceeds the measure of
each base angle by 30. Find the measure of each angle of the triangle.
Example 2:
In triangle ABC, m<A = 9x, m<B = 3x – 6, m<C = 11x+2, show that triangle ABC is a
right triangle.
Example 3:
Triangle ABC is an isosceles triangle, where AC  BC . If AC  4x  1 ,
AB  9x  1 , and BC  5x  0.5 , what is the measure of each side of the triangle?
Example 4:
Given equilateral triangle FGH with FG  2y  5 , GH  3y  3 , and FH  5y  19 ,
what is the measure of each side of the triangle?
Example 5:
The measure of the larger acute angle in a right triangle is two degrees less than
three times the measure of the smaller acute angle. Find the measure of each
angle.
Examples:
Complete all work on a separate sheet of paper.
1. Find the measures of the angles of a triangle if the ratio between the
measures is 4:3:2. How can we classify this triangle?
2. Can 55, 45, and 90 represent the measures of the three angles in a triangle?
3. Find the measures of each angle of a triangle if the ratio of the measures is
2:5:2. How can we classify this triangle?
4. The measures of two angles of a triangle are in the ratio 3:4. The measure
of the third angle is 20 more than the measure of the smaller of the first
two angles. Find the measure of each angle.
5. The measure of the vertex angle of an isosceles triangle is three times the
measure of each base angle. Find the measure of each angle.
6. Each of the congruent angles of an isosceles triangle measures 9 less than
four times the vertex angle. Find the measures of the angles of the triangle.
7. In triangle ABC, mA  80 , mB  50 . If AB  4x  4 and AC  2x  16 ,
find AB and AC .
8. The measures of the angles of a triangle are represented by x  35 ,
2x  10 , and 3x  15 .
a. Express the sum of the measures of the angles in terms of x.
b. Find the value of x.
c. Show that the triangle is equilateral.
9. ΔFGH is equilateral with FG  3x  10 , GH  2x  5 , and HF  x  20 . Find
the value of x and the measure of each side of the triangle. How can we
classify this triangle?
10. ΔJKL is isosceles with JK  KL , JK  4x  1 , KL  2x  5 , and LJ  2x  1 .
Find the value of x and the measure of each side of the triangle.