1. Classifying Triangles
By angles
Acute- all angle measures < 90
Obtuse- one angle measure > 90
Right- one angle = 90
Equiangular- all angle measures are equal
By sides
Scalene- no two sides are congruent
Isosceles- at least two sides are congruent
Equilateral- all sides are congruent

2. ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right.
Example 1-1a

3. Answer:
JMN has one angle with measure greater than 90, so it is an obtuse triangle.
JKO has one angle with measure equal to 90, so it is a right triangle.
OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.
Example 1-1a

4. Answer: ABC is acute. ACD is obtuse. ADE is right.
ARCHITECTURE The frame of this window design is made up of many triangles. Classify ABC, ACD, and ADE as acute, equiangular, obtuse, or right.
Answer: ABC is acute. ACD is obtuse. ADE is right.
Example 1-1b

5. Identify the isosceles triangles in the figure if
Isosceles triangles have at least two sides congruent.
Answer: UTX and UVX are isosceles.
Example 1-2a

6. Identify the scalene triangles in the figure if
Scalene triangles have no congruent sides.
Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.
Example 1-2b

7. Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD
Example 1-2c

8. Since KLM is equilateral, each side has the same length. So
ALGEBRA Find d and the measure of each side of equilateral triangle KLM if and
Since KLM is equilateral, each side has the same length. So
Substitution
Subtract d from each side.
Add 13 to each side.
Divide each side by 3.
Example 1-3a

9. Next, substitute to find the length of each side.
Answer: For KLM, and the measure of each side is 7.
Example 1-3b

10. ALGEBRA Find x and the measure of each side of equilateral triangle if
ALGEBRA Find x and the measure of each side of equilateral triangle if and
Answer:
Example 1-3c

11. COORDINATE GEOMETRY Find the measures of the sides of RST
COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.
Example 1-4a

12. Use the distance formula to find the lengths of each side.
Answer: ; since all 3 sides have different lengths, RST is scalene.
Example 1-4b

13. Answer: ; since all 3 sides have different lengths, ABC is scalene.
Find the measures of the sides of ABC. Classify the triangle by sides.
Answer: ; since all 3 sides have different lengths, ABC is scalene.
Example 1-4c