Classifying 2D Shapes — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A triangle has two angles of 55° each. Classify it by both sides and angles.
A) Scalene acute
B) Isosceles obtuse
C) Isosceles acute
D) Equilateral acute
Two equal angles (55°) mean two equal sides → isosceles. Third angle = 180−55−55=70°. All angles < 90° → acute. Classification: isosceles acute.
2. Which of the following is NOT possible?
A) A right scalene triangle
B) An obtuse equilateral triangle
C) An acute isosceles triangle
D) A right isosceles triangle
An obtuse equilateral triangle is impossible. An equilateral triangle has all angles equal to 60°, which are all acute. It cannot have an obtuse angle and still be equilateral.
3. A triangle has angles of 90°, 45°, and 45°. Which classification best describes it?
A) Scalene right
B) Equilateral acute
C) Isosceles right
D) Isosceles obtuse
Two equal angles (45°) mean two equal sides → isosceles. One angle is exactly 90° → right triangle. Classification: isosceles right.
4. Triangle PQR has sides 6 cm, 6 cm, and 6 cm. What is the measure of each angle?
A) 90°
B) 45°
C) 60°
D) 120°
Three equal sides → equilateral triangle. All angles are equal and sum to 180°. Each angle = 180° ÷ 3 = 60°.
Part B: Fill in the Blank
Write the correct answer on each line.
1. If two angles of a triangle are 70° each, the third angle is 40 degrees.
Angles sum to 180°. 70 + 70 = 140. Third angle = 180 − 140 = 40°.
2. A triangle with angles 40°, 60°, and 80° is classified as acute by its angles.
All three angles (40°, 60°, 80°) are less than 90°, so the triangle is acute. They sum to 180° ✓.
3. A triangle with sides 7 cm, 7 cm, and 10 cm is isosceles by its sides and obtuse by its angles.
Two equal sides (7,7) → isosceles. The longer side (10) is opposite a large angle. Using the law of cosines or the fact that 7²+7²=98 < 10²=100 confirms one obtuse angle.
4. The largest angle in a right triangle always measures exactly 90 degrees.
In a right triangle, the right angle (90°) is the largest angle. The other two angles are both acute and sum to 90°.
5. If one angle of a triangle is 90° and another is 35°, the third angle is 55 degrees.
Angles sum to 180°. 90 + 35 = 125. Third angle = 180 − 125 = 55°.