Classifying Triangles — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which triangle is impossible?
A) Right scalene
B) Right equilateral
C) Acute isosceles
D) Obtuse scalene
An equilateral triangle always has three 60 degree angles, so it cannot also have a 90 degree right angle.
2. A triangle has angles 25, 65, and 90 degrees. Classify it.
A) Acute scalene
B) Right scalene
C) Right isosceles
D) Obtuse isosceles
The 90 degree angle makes it a right triangle, and three different angles mean three different sides, so it is scalene.
3. Which set of side lengths describes an isosceles triangle?
A) 3 cm, 4 cm, 5 cm
B) 5 cm, 5 cm, 5 cm
C) 6 cm, 6 cm, 8 cm
D) 7 cm, 9 cm, 11 cm
Sides 6 cm, 6 cm, and 8 cm have exactly two equal sides, which is the definition of isosceles.
4. Two angles of a triangle measure 55 and 55 degrees. What kind of triangle must it be?
A) Right scalene
B) Obtuse isosceles
C) Acute isosceles
D) Equilateral
The third angle is 180 minus 55 minus 55, which equals 70; all angles are below 90 and two are equal, so it is acute isosceles.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A triangle has angles 45, 60, and 75 degrees.
180 minus 45 minus 60 equals 75, so the third angle is 75 degrees and the triangle is acute scalene.
2. A triangle has angles 30, 30, and 120 degrees, making it obtuse isosceles.
180 minus 30 minus 30 equals 120; one angle is greater than 90 (obtuse) and two are equal (isosceles).
3. A right triangle with two equal legs has angles of 90, 45, and 45 degrees.
After 90 degrees, the remaining 90 degrees splits equally into two 45 degree angles because the legs are equal.
4. If a triangle has angles 70, 70, and 40 degrees, it is an acute isosceles triangle.
Two equal 70 degree angles make the triangle isosceles, and all angles below 90 make it acute.
5. A triangle with angles 100, 50, and 30 degrees is an obtuse scalene triangle by side lengths.
Each angle is different, so each opposite side is a different length, making the triangle scalene.