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 one 90 degree angle is called an acute triangle.
Corrected: A triangle with one 90 degree angle is called a right triangle.
A right triangle has exactly one right angle, which measures 90 degrees, like the corner of a book.
2. Fix the sentence:
If all three angles in a triangle are less than 90 degrees, the triangle is obtuse.
Corrected: If all three angles in a triangle are less than 90 degrees, the triangle is acute.
An acute triangle has all three angles smaller than 90 degrees; an obtuse triangle has one angle bigger than 90 degrees.
3. Fix the sentence:
A triangle that has one angle measuring 120 degrees is a right triangle.
Corrected: A triangle that has one angle measuring 120 degrees is an obtuse triangle.
Any triangle with one angle larger than 90 degrees is an obtuse triangle, since obtuse angles are greater than a right angle.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A triangle with exactly one 90 degree angle is called a right triangle.
A right triangle has one 90 degree angle, the kind you see at the corner of a book.
2. A triangle in which every angle measures less than 90 degrees is called an acute triangle.
When all three angles are below 90 degrees, the triangle is classified as acute.
3. A triangle with one angle that is greater than 90 degrees is called an obtuse triangle.
An obtuse triangle has exactly one angle larger than 90 degrees and two smaller angles.
4. The point where two sides of a triangle meet is called a vertex.
A vertex is the corner of a triangle where two sides meet; every triangle has three vertices.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how to decide if a triangle is acute, right, or obtuse.
Sample answer: Look at the three angles of the triangle. If every angle is less than 90 degrees, it is acute. If one angle is exactly 90 degrees, it is right. If one angle is greater than 90 degrees, it is obtuse.
Triangles are classified by angle by checking each angle against 90 degrees: less than, equal to, or greater than.
2. Why can a triangle have only one right angle or only one obtuse angle?
Sample answer: All three angles in a triangle add up to 180 degrees. If two angles were 90 degrees or more, they alone would equal at least 180 degrees, leaving nothing for the third angle.
Because the three angles must sum to 180 degrees, only one angle can be 90 degrees or larger; the other two must be acute.