Classifying Triangles — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Maya is designing a triangular garden where all three sides must be 8 feet. Which classification fits her garden?
A) Equilateral and acute
B) Isosceles and right
C) Scalene and obtuse
D) Equilateral and obtuse
Three congruent sides give three 60 degree angles, so the triangle is equilateral and acute.
2. Which set of angles cannot form a triangle?
A) 60, 60, 60
B) 90, 45, 45
C) 100, 50, 40
D) 80, 70, 30
100 plus 50 plus 40 equals 190, which is more than 180, so these angles cannot form a triangle.
3. A roof truss has two sides of 10 feet and one side of 6 feet. What is its classification by sides?
A) Equilateral
B) Isosceles
C) Scalene
D) Right
When exactly two sides of a triangle are equal, the triangle is classified as isosceles by sides.
4. Can a triangle be both right and obtuse at the same time?
A) Yes, if it has two 90 degree angles
B) Yes, if one angle is 90 and one is 100
C) No, because the angles would sum to more than 180
D) No, because right triangles have no 90 degree angle
A 90 degree plus a greater than 90 degree angle already exceeds 180, so a triangle cannot be both right and obtuse.
Part B: Fill in the Blank
Write the correct answer on each line.
1. If all three sides of a triangular sign are 12 inches, the triangle is classified as equilateral.
Three congruent sides always classify a triangle as equilateral.
2. A triangle with sides 5, 5, 5 has angles that each measure 60 degrees.
An equilateral triangle has three congruent angles, and 180 divided by 3 equals 60 degrees.
3. A set of angles 95, 50, and 35 degrees forms a(n) obtuse triangle.
Because one angle is greater than 90 degrees, the triangle is classified as obtuse.
4. A triangle cannot have two angles each measuring more than 90 degrees at the same time.
Two angles greater than 90 already sum to more than 180, but a triangle's angles must sum to exactly 180 degrees.
5. A triangle with angles 70, 70, and 40 has two equal angles, so its sides also include two congruent sides.
Equal angles in a triangle are opposite congruent sides, so this isosceles triangle has two congruent sides.