Classifying Triangles — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The three angles of any triangle always add up to 180 degrees.
The angle-sum property says the three angles inside any triangle add to 180 degrees.
2. A triangle has angles of 50, 60, and 70 degrees.
180 minus 50 minus 60 equals 70, so the missing angle is 70 degrees.
3. A triangle has a 90 degree angle and three sides of different lengths. It is a right scalene triangle.
The triangle is right because of its 90 degree angle and scalene because all three sides have different lengths.
4. Every equilateral triangle is also an acute triangle, because all its angles are less than 90 degrees.
An equilateral triangle has three 60 degree angles, all less than 90 degrees, so it is always acute.
5. If a triangle has angles of 100, 40, and 40 degrees, it is an obtuse isosceles triangle.
Two angles are equal at 40 degrees, so the triangle is isosceles, and one angle of 100 degrees makes it obtuse.
6. A right triangle can have its two shorter sides equal in length, making it a right isosceles triangle.
When the two legs of a right triangle are the same length, it is both right and isosceles.
7. If two angles of a triangle measure 35 and 55 degrees, the third angle is 90 degrees.
180 minus 35 minus 55 equals 90, so the third angle is 90 degrees, making the triangle a right triangle.
8. A triangle that has all three angles less than 90 degrees is called an acute triangle.
An acute triangle has every angle measuring less than 90 degrees.
9. Angles of 70, 70, and 40 degrees describe an isosceles triangle (by sides) that is also acute.
Because two angles are equal at 70 degrees, the two opposite sides are also equal, so the triangle is isosceles.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
Triangle with all sides equal
→ Equilateral triangle
Right triangle
Triangle with one 90 degree angle
→ Right triangle
Equilateral triangle
Triangle with one angle greater than 90 degrees
→ Obtuse triangle
Scalene triangle
Triangle with all three sides different lengths
→ Scalene triangle
Obtuse triangle
Each triangle name comes from either an angle measure (right, obtuse) or a count of equal sides (equilateral, scalene).