Students correct three triangle classification errors — equilateral having two equal sides, a right triangle having all angles under 90°, and scalene having at least two equal sides. Part B has four questions about equilateral, obtuse, and isosceles triangles. Part C has two questions about right-isosceles triangles and classifying a 60°-60°-60° triangle.
Correcting the three most common triangle classification errors — equilateral, right, and scalene — establishes the accurate definitions students need before classifying from angle or side measurements.
Style:
Classifying 2D Shapes
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.
Rewrite: An equilateral triangle has three equal sides and three equal angles of 60°.
2. Fix the sentence:
A right triangle has all angles less than 90°.
Rewrite: A right triangle has exactly one angle equal to 90°.
3. Fix the sentence:
A scalene triangle has at least two equal sides.
Rewrite: A scalene triangle has no equal sides and no equal angles.
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.
2. A triangle with exactly one angle greater than 90° is called a(n) obtuse triangle.
3. An isosceles triangle has exactly 2 equal sides.
4. The sum of all interior angles in any triangle is 180 degrees.
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.
Yes. A right isosceles triangle has one 90° angle and two equal sides, with the two remaining angles each measuring 45°.
2. A triangle has angles measuring 60°, 60°, and 60°. Classify this triangle by both its sides and its angles.
It is an equilateral triangle because all three sides are equal. It is also an acute triangle because all angles are less than 90°.
Classifying 2D Shapes
★ 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.
Rewrite: An equilateral triangle has three equal sides and three equal angles of 60°.
2) Fix the sentence:
A right triangle has all angles less than 90°.
Rewrite: A right triangle has exactly one angle equal to 90°.
3) Fix the sentence:
A scalene triangle has at least two equal sides.
Rewrite: A scalene triangle has no equal sides and no equal angles.
★ 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.
2) A triangle with exactly one angle greater than 90° is called a(n) obtuse triangle.
3) An isosceles triangle has exactly 2 equal sides.
4) The sum of all interior angles in any triangle is 180 degrees.
★ 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.
Yes. A right isosceles triangle has one 90° angle and two equal sides, with the two remaining angles each measuring 45°.
2) A triangle has angles measuring 60°, 60°, and 60°. Classify this triangle by both its sides and its angles.
It is an equilateral triangle because all three sides are equal. It is also an acute triangle because all angles are less than 90°.
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9 Questions
15-20 minutes
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