Classifying Triangles — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. A triangle with three congruent sides and three 60 degree angles is equilateral and acute.
Equilateral triangles always have three 60 degree angles, which makes them acute as well.
2. A triangle with two congruent sides and a 90 degree angle is isosceles and right.
An isosceles right triangle has two congruent legs and a 90 degree angle between them.
3. A triangle with three different side lengths and one 110 degree angle is scalene and obtuse.
Scalene triangles have no congruent sides, and an angle above 90 degrees makes them obtuse.
4. A triangle with sides 4, 4, 4 and angles 60, 60, 60 can be classified as equilateral and acute.
Every angle in this triangle is 60, which is less than 90, so it is acute.
5. A triangle with two equal sides and a 100 degree vertex angle is isosceles and obtuse.
When an isosceles triangle has one angle greater than 90, it is obtuse as well as isosceles.
6. A triangle with three different sides and three angles of 50, 60, and 70 is scalene and acute.
Since every angle in this triangle measures less than 90 degrees, it is acute, and unequal sides make it scalene.
7. A triangle with two congruent sides and three angles of 70, 70, and 40 is isosceles and acute.
All three angles are below 90 degrees, so the triangle is acute, and the two congruent sides make it isosceles.
8. A triangle with three different sides and a 90 degree angle is scalene and right.
A right triangle contains one 90 degree angle, and three unequal sides make it scalene.
9. A triangle with sides 6, 6, 8 and angles 70, 70, 40 is isosceles and acute.
Two congruent sides classify it as isosceles, and three angles below 90 make it acute.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
Equilateral with all 60 degree angles
→ Equilateral and acute
Equilateral and acute
Isosceles with a 90 degree angle
→ Isosceles and right
Isosceles and right
Scalene with a 120 degree angle
→ Scalene and obtuse
Scalene and obtuse
Scalene with angles 50, 60, 70
→ Scalene and acute
Scalene and acute
Triangles can be named two ways at once: by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse).