Classifying Triangles — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The corner of a piece of paper measures 60 degrees, so a triangle with that angle is acute.
Corrected: The corner of a piece of paper measures 90 degrees, so a triangle with that angle is a right triangle.
Paper corners are right angles measuring 90 degrees, which makes any triangle containing one a right triangle.
2. Fix the sentence:
A triangle whose largest angle measures 110 degrees is classify as an acute triangle.
Corrected: A triangle whose largest angle measures 110 degrees is classified as an obtuse triangle.
An obtuse triangle has exactly one angle greater than 90 degrees, while acute triangles have all angles below 90.
3. Fix the sentence:
If all three angles in a triangle measure less than 90 degrees, the triangle is a right triangle.
Corrected: If all three angles in a triangle measure less than 90 degrees, the triangle is an acute triangle.
Acute triangles have every angle less than 90 degrees; right triangles must contain one 90 degree angle.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The corner of a piece of paper forms a right angle that measures 90 degrees.
Right angles measure exactly 90 degrees and look like the perfect corner of a sheet of paper.
2. A triangle that contains exactly one 90 degree angle is called a right triangle.
Right triangles are named for the 90 degree right angle they contain at one vertex.
3. When the hour hand points to 12 and the minute hand points to 3, the hands form a right angle.
A quarter turn on a clock equals 90 degrees, which is a right angle.
4. A triangle with one angle measuring 120 degrees must be classified as an obtuse triangle.
Any triangle with an angle larger than 90 degrees is obtuse, because only one such angle can fit in a triangle.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How can the corner of a piece of paper help you decide if a triangle has a right angle?
Sample answer: I can place the paper corner against a triangle vertex. If it fits exactly, that angle is 90 degrees, so the triangle is a right triangle.
Paper corners are reliable 90 degree references because they are manufactured as right angles.
2. A clock shows 9:00. What kind of angle do the hour and minute hands form, and why?
Sample answer: At 9:00 the hands form a right angle of 90 degrees because the minute hand points to 12 and the hour hand points to 9, making a quarter turn apart.
Three hours of separation on a clock equals 90 degrees, since 3 times 30 equals 90.