Classifying Triangles — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A triangle with all three sides the same length is called an isosceles triangle.
Corrected: A triangle with all three sides the same length is called an equilateral triangle.
An equilateral triangle has all three sides equal in length; an isosceles triangle has only two equal sides.
2. Fix the sentence:
A triangle with no sides the same length is called an equilateral triangle.
Corrected: A triangle with no sides the same length is called a scalene triangle.
A scalene triangle has three sides of different lengths and three different angle measures.
3. Fix the sentence:
An isosceles triangle has three sides of different lengths.
Corrected: An isosceles triangle has two sides of equal length.
An isosceles triangle has exactly two sides the same length and the angles opposite those sides are equal.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A triangle with all three sides the same length is called an equilateral triangle.
An equilateral triangle has three equal sides and three equal 60 degree angles.
2. A triangle with exactly two sides the same length is called an isosceles triangle.
An isosceles triangle has two equal sides, and the angles opposite those equal sides are also equal.
3. A triangle with no sides the same length is called a scalene triangle.
A scalene triangle has three sides of different lengths and three angles of different measures.
4. Each angle of an equilateral triangle measures 60 degrees.
Since the angles of any triangle add to 180 degrees and an equilateral triangle has three equal angles, each one is 180 divided by 3, or 60 degrees.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How can you classify a triangle by looking only at its side lengths?
Sample answer: Compare the three side lengths. If all three are equal, the triangle is equilateral. If exactly two are equal, it is isosceles. If all three are different, it is scalene.
Triangles are classified by side using how many sides match: three equal, two equal, or none equal.
2. Why is every equilateral triangle also an isosceles triangle in some definitions, but a scalene triangle is never equilateral?
Sample answer: Equilateral triangles have three equal sides, which means they also have at least two equal sides, fitting the isosceles description. Scalene triangles have no equal sides, so they cannot have all three equal.
Equilateral triangles meet the at-least-two-equal-sides rule for isosceles, while scalene means zero equal sides, the opposite of equilateral.