Q1: A triangle has three sides that are all the same length. What type of triangle is it? (a) Scalene triangle (b) Isosceles triangle (c) Equilateral triangle (d) Right triangle
Solution:
Ans: (c) Explanation: An equilateral triangle has all three sides equal in length. A scalene triangle has all different sides, an isosceles triangle has exactly two equal sides, and a right triangle is classified by its angle, not side length.
Q2: Which triangle has exactly two sides of equal length? (a) Equilateral triangle (b) Scalene triangle (c) Isosceles triangle (d) Obtuse triangle
Solution:
Ans: (c) Explanation: An isosceles triangle has exactly two sides that are equal in length. An equilateral triangle has all three sides equal, a scalene triangle has no equal sides, and an obtuse triangle is classified by its angle.
Q3: A triangle has sides measuring 5 cm, 7 cm, and 9 cm. What type of triangle is this based on its sides? (a) Equilateral triangle (b) Isosceles triangle (c) Scalene triangle (d) Right triangle
Solution:
Ans: (c) Explanation: A scalene triangle has all three sides of different lengths. Since \(5 \neq 7 \neq 9\), none of the sides are equal, making this a scalene triangle.
Q4: A triangle has one angle that measures exactly 90 degrees. What type of triangle is it? (a) Acute triangle (b) Right triangle (c) Obtuse triangle (d) Equilateral triangle
Solution:
Ans: (b) Explanation: A right triangle has one angle that measures exactly 90 degrees. An acute triangle has all angles less than 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.
Q5: All angles in a triangle measure less than 90 degrees. What type of triangle is this? (a) Right triangle (b) Obtuse triangle (c) Acute triangle (d) Scalene triangle
Solution:
Ans: (c) Explanation: An acute triangle has all three angles measuring less than 90 degrees. A right triangle has one 90-degree angle, and an obtuse triangle has one angle greater than 90 degrees.
Q6: A triangle has one angle that measures 120 degrees. What type of triangle is it based on its angles? (a) Acute triangle (b) Right triangle (c) Obtuse triangle (d) Equilateral triangle
Solution:
Ans: (c) Explanation: An obtuse triangle has one angle that measures greater than 90 degrees. Since 120 degrees is greater than 90 degrees, this is an obtuse triangle.
Q7: Which statement is true about an equilateral triangle? (a) It has two equal sides and one different side (b) It has all angles equal to 60 degrees (c) It has one angle equal to 90 degrees (d) It has all sides of different lengths
Solution:
Ans: (b) Explanation: An equilateral triangle has all three sides equal and all three angles equal to 60 degrees. This is a special property of equilateral triangles where both sides and angles are equal.
Q8: A triangle has angles measuring 45 degrees, 45 degrees, and 90 degrees. What can you say about this triangle? (a) It is both a right triangle and an isosceles triangle (b) It is only an acute triangle (c) It is both an obtuse triangle and a scalene triangle (d) It is only an equilateral triangle
Solution:
Ans: (a) Explanation: This triangle has one 90-degree angle, making it a right triangle. It also has two equal angles (45 degrees each), which means it has two equal sides, making it an isosceles triangle. A triangle can be classified in more than one way.
Section B: Fill in the Blanks
Q9: A triangle with all three sides of different lengths is called a __________ triangle.
Solution:
Ans: scalene Explanation: A scalene triangle is defined as a triangle where all three sides have different lengths and all three angles are different.
Q10: A triangle with all three sides equal in length is called an __________ triangle.
Solution:
Ans: equilateral Explanation: An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees.
Q11: A triangle that has one angle measuring exactly 90 degrees is called a __________ triangle.
Solution:
Ans: right Explanation: A right triangle contains one angle that measures exactly 90 degrees, which is called a right angle.
Q12: A triangle with one angle greater than 90 degrees is called an __________ triangle.
Solution:
Ans: obtuse Explanation: An obtuse triangle has one angle that measures greater than 90 degrees but less than 180 degrees.
Q13: A triangle with exactly two sides of equal length is called an __________ triangle.
Solution:
Ans: isosceles Explanation: An isosceles triangle has exactly two sides that are equal in length, and the angles opposite these equal sides are also equal.
Q14: A triangle with all three angles measuring less than 90 degrees is called an __________ triangle.
Solution:
Ans: acute Explanation: An acute triangle has all three angles measuring less than 90 degrees. Each angle is called an acute angle.
Section C: Word Problems
Q15: Sarah drew a triangle with sides measuring 6 inches, 6 inches, and 8 inches. What type of triangle did Sarah draw based on its sides?
Solution:
Ans: Step 1: Look at the side lengths: 6 inches, 6 inches, and 8 inches. Step 2: Two sides are equal (both 6 inches), but one side is different (8 inches). Step 3: A triangle with exactly two equal sides is an isosceles triangle. Final Answer: Isosceles triangle
Q16: Michael is building a triangular frame for his art project. All three sides of the triangle measure 10 centimeters each. What type of triangle is Michael's frame?
Solution:
Ans: Step 1: All three sides measure 10 cm each. Step 2: When all three sides are equal, the triangle is an equilateral triangle. Final Answer: Equilateral triangle
Q17: A triangular traffic sign has angles measuring 50 degrees, 60 degrees, and 70 degrees. What type of triangle is the sign based on its angles?
Solution:
Ans: Step 1: Check each angle: 50 degrees, 60 degrees, and 70 degrees. Step 2: All three angles are less than 90 degrees. Step 3: A triangle with all angles less than 90 degrees is an acute triangle. Final Answer: Acute triangle
Q18: Emma measured the angles of a triangular piece of paper. She found that one angle measures 90 degrees, and the other two angles measure 45 degrees each. How can Emma classify this triangle based on both its angles and sides?
Solution:
Ans: Step 1: One angle is 90 degrees, so it is a right triangle. Step 2: Two angles are equal (both 45 degrees), which means two sides are equal. Step 3: A triangle with two equal sides is an isosceles triangle. Final Answer: Right isosceles triangle (or isosceles right triangle)
Q19: A triangular garden has sides measuring 12 feet, 15 feet, and 18 feet. What type of triangle is the garden based on its sides?
Solution:
Ans: Step 1: Look at the side lengths: 12 feet, 15 feet, and 18 feet. Step 2: All three sides have different measurements. Step 3: A triangle with all different side lengths is a scalene triangle. Final Answer: Scalene triangle
Q20: A triangular flag has one angle that measures 110 degrees. The other two angles are smaller. What type of triangle is the flag based on its angles?
Solution:
Ans: Step 1: One angle measures 110 degrees. Step 2: Since 110 degrees is greater than 90 degrees, this is the obtuse angle. Step 3: A triangle with one angle greater than 90 degrees is an obtuse triangle. Final Answer: Obtuse triangle
The document Worksheet (with Solutions): Classifying Triangles is a part of the Grade 4 Course Math Grade 4.
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