Classifying 2D Shapes — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
An equilateral triangle has two equal sides and one different side.
Corrected: An equilateral triangle has three equal sides and three equal angles of 60°.
The corrected sentence is: "An equilateral triangle has three equal sides and three equal angles of 60°.". The original sentence "An equilateral triangle has two equal sides and one different side." contained an error that needed to be fixed.
2. Fix the sentence:
A right triangle has all angles less than 90°.
Corrected: A right triangle has exactly one angle equal to 90°.
The corrected sentence is: "A right triangle has exactly one angle equal to 90°.". The original sentence "A right triangle has all angles less than 90°." contained an error that needed to be fixed.
3. Fix the sentence:
A scalene triangle has at least two equal sides.
Corrected: A scalene triangle has no equal sides and no equal angles.
The corrected sentence is: "A scalene triangle has no equal sides and no equal angles.". The original sentence "A scalene triangle has at least two equal sides." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A triangle with all three sides equal is called a(n) equilateral triangle.
An equilateral triangle has three equal sides and three equal angles (each 60°). 'Equilateral' comes from Latin meaning 'equal sides.'
2. A triangle with exactly one angle greater than 90° is called a(n) obtuse triangle.
An obtuse triangle has exactly one angle measuring more than 90°. Since the angles must sum to 180°, there can be at most one obtuse angle.
3. An isosceles triangle has exactly 2 equal sides.
An isosceles triangle has exactly two equal sides (called legs) and two equal base angles opposite those sides.
4. The sum of all interior angles in any triangle is 180 degrees.
The Triangle Angle Sum Theorem states that the interior angles of any triangle always add up to exactly 180°.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Can a triangle be both right and isosceles at the same time? Explain why or why not.
Sample answer: Yes. A right isosceles triangle has one 90° angle and two equal sides, with the two remaining angles each measuring 45°.
A right isosceles triangle is possible: the right angle is 90° and the other two angles are each 45°, giving equal legs opposite the two 45° angles.
2. A triangle has angles measuring 60°, 60°, and 60°. Classify this triangle by both its sides and its angles.
Sample answer: It is an equilateral triangle because all three sides are equal. It is also an acute triangle because all angles are less than 90°.
When all angles are equal (60° each), all sides must also be equal — making it equilateral by sides. All angles are less than 90°, making it acute by angles.