CBSE Class 5 Mathematics Triangle Worksheet

Ln. 19 : TRIANGLE

I. Fill in the blanks :

Question 1. A figure bounded by three line segments is called __________________ .
Answer: triangle
In simple words: A closed geometric shape made of three straight line segments is a triangle.

Exam Tip: Remember that a polygon with the least number of sides is a triangle.

Question 2. The intersection of two sides of a triangle is called a __________________ of the triangle.
Answer: vertex
In simple words: The corner point where two sides meet is the vertex.

Exam Tip: A triangle has three vertices corresponding to its three corners.

Question 3. A triangle has __________________ sides.
Answer: three
In simple words: Tri- means three, so a triangle always has three sides.

Exam Tip: Count the line segments forming the boundary to identify the number of sides.

Question 4. A triangle has __________________ angles.
Answer: three
In simple words: The interior corners form three angles.

Exam Tip: The number of sides always equals the number of interior angles in any polygon.

Question 5. A triangle has __________________ vertices.
Answer: three
In simple words: A triangle has three corner points.

Exam Tip: Vertices are denoted by capital letters like A, B, and C.

Question 6. The line segments AB, BC and CA are called __________________ of the triangle.
Answer: sides
In simple words: The straight edges joining the vertices are the sides.

Exam Tip: Named using their endpoint vertices with a bar or plain letters.

Question 7. A triangle which has all its sides of different length is called a _________________ triangle.
Answer: scalene
In simple words: When no sides are equal, it is a scalene triangle.

Question 8. A triangle is called _________________ if it has an angle of measure \(90^\circ\).
Answer: right-angled
In simple words: A triangle with one right angle is a right-angled triangle.

Exam Tip: The side opposite to the right angle is the longest side, called the hypotenuse.

Question 9. The sum of the measures of three angles is _________________.
Answer: \(180^\circ\)
In simple words: The interior angles of any triangle always add up to \(180^\circ\).

Exam Tip: This is known as the angle sum property of a triangle.

Question 10. A triangle cannot have more than one _________________ angle.
Answer: obtuse (or right)
In simple words: Since the sum of angles is \(180^\circ\), you can only fit one angle greater than or equal to \(90^\circ\).

Exam Tip: Keep this rule in mind when checking if angle combinations form a valid triangle.

Question 11. A triangle whose two sides are equal is called an _________________ triangle.
Answer: isosceles
In simple words: A triangle with two equal sides is an isosceles triangle.

Exam Tip: Angles opposite to the equal sides are also equal.

Question 12. Each angle of an equilateral triangle is _________________.
Answer: \(60^\circ\)
In simple words: All three angles are equal, so each is \(180^\circ \div 3 = 60^\circ\).

Exam Tip: Equilateral triangles are also equiangular.

Question 13. The side opposite to the right angle is called the _________________.
Answer: hypotenuse
In simple words: The longest side facing the \(90^\circ\) angle is the hypotenuse.

Exam Tip: Applicable exclusively in right-angled triangles.

Question 14. A triangle is called _________________ if all its angles are acute.
Answer: acute-angled
In simple words: When every angle is less than \(90^\circ\), it is acute-angled.

Exam Tip: Acute means sharp or less than a right angle.

Question 15. The sum of the lengths of any two sides of a triangle is _________________ than the length of the third side.
Answer: greater
In simple words: The path straight across (third side) is always shorter than going around the other two sides.

Exam Tip: This is the fundamental triangle inequality property.

Question 16. A triangle whose three sides are equal is called an _________________ triangle.
Answer: equilateral
In simple words: Equal sides mean an equilateral triangle.

Exam Tip: "Equi" means equal and "lateral" means side.

Question 17. A triangle is called right angled if _________________.
Answer: one of its angles is \(90^\circ\)
In simple words: Having a single right angle makes it a right-angled triangle.

Exam Tip: Look for the square corner symbol in diagrams.

Question 18. If in the \(\Delta\) ABC, AB = BC = CA, then \(\Delta\) ABC is _______________
Answer: an equilateral triangle
In simple words: All three sides being equal defines an equilateral triangle.

Question 19. If in the \(\Delta\) PQR, PQ = PR then \(\Delta\) PQR is _______________
Answer: an isosceles triangle
In simple words: Two equal sides mean an isosceles triangle.

Exam Tip: The angles opposite to PQ and PR (namely \(\angle R\) and \(\angle Q\)) are also equal.

Question 20. If in the \(\Delta\) XYZ, \(\angle Y = 90^\circ\), then the hypotenuse is _____________.
Answer: XZ
In simple words: The side opposite to angle Y is XZ, which is the hypotenuse.

Exam Tip: The hypotenuse is always the side that does not contain the right-angle vertex.

Question 21. If in the \(\Delta\) ABC, \(\angle A = 60^\circ\), and \(\angle C = 30^\circ\), then the triangle is ______________
Answer: a right-angled triangle
In simple words: Find angle B as \(180^\circ - (60^\circ + 30^\circ) = 90^\circ\), making it right-angled.

Exam Tip: Always calculate the third unknown angle first.

Question 22. A triangle is called ______________ .
Answer: a polygon with three sides (or classified by sides/angles)
In simple words: General definition of a triangle based on its geometric properties.

Exam Tip: Ensure complete terminology is used if specific blanks require classification.

Question 23. In \(\angle PQR\) the vertex is _____________ and the arms are _____________ and _____________.
Answer: Q; QP; QR
In simple words: The middle letter Q is the vertex, and rays QP and QR form the arms.

Exam Tip: The vertex is always the middle letter in a three-letter angle notation.

II. Subjective type question :

Question 1. In \(\Delta\) ABC, if \(\angle A = 40^\circ\), and \(\angle B = 80^\circ\), then find \(\angle C = ?\)
Answer:
Sum of angles in \(\Delta\) ABC = \(180^\circ\)
\(\angle A + \angle B + \angle C = 180^\circ\)
\(40^\circ + 80^\circ + \angle C = 180^\circ\)
\(120^\circ + \angle C = 180^\circ\)
\(\angle C = 180^\circ - 120^\circ = 60^\circ\)
In simple words: Subtract the sum of the two given angles from \(180^\circ\) to find the third angle.

Exam Tip: Always state the angle sum property formula before substituting values.

Question 2. In an isosceles \(\Delta\) XYZ, if \(\angle X = \angle Y = 70^\circ\), then find \(\angle Z = ?\)
Answer:
Sum of angles in \(\Delta\) XYZ = \(180^\circ\)
\(\angle X + \angle Y + \angle Z = 180^\circ\)
\(70^\circ + 70^\circ + \angle Z = 180^\circ\)
\(140^\circ + \angle Z = 180^\circ\)
\(\angle Z = 180^\circ - 140^\circ = 40^\circ\)
In simple words: Add the two equal angles and subtract from \(180^\circ\).

Exam Tip: Double-check your addition \(70 + 70 = 140\) before subtraction.

Question 3. In \(\Delta\) XYZ, \(\angle X = \angle Y = \angle Z\) find each of them.
Answer:
Let each angle be \(x\).
\(\angle X + \angle Y + \angle Z = 180^\circ\)
\(x + x + x = 180^\circ\)
\(3x = 180^\circ\)
\(x = \frac{180^\circ}{3} = 60^\circ\)
Each angle is \(60^\circ\).
In simple words: Divide the total sum \(180^\circ\) equally among the three identical angles.

Exam Tip: An equiangular triangle is always an equilateral triangle.

Question 4. In \(\Delta\) PQR, if \(\angle Q = \angle R\) and \(\angle P = 90^\circ\), then find \(\angle Q =\) and \(\angle R\).
Answer:
Sum of angles in \(\Delta\) PQR = \(180^\circ\)
\(\angle P + \angle Q + \angle R = 180^\circ\)
\(90^\circ + \angle Q + \angle Q = 180^\circ\) (since \(\angle Q = \angle R\))
\(90^\circ + 2\angle Q = 180^\circ\)
\(2\angle Q = 180^\circ - 90^\circ\)
\(2\angle Q = 90^\circ\)
\(\angle Q = \frac{90^\circ}{2} = 45^\circ\)
Therefore, \(\angle Q = 45^\circ\) and \(\angle R = 45^\circ\).
In simple words: Subtract the \(90^\circ\) right angle from \(180^\circ\) and divide the remaining \(90^\circ\) equally into two halves.

Exam Tip: This describes an isosceles right-angled triangle.

Question 5. In which of the following cases is a triangle possible with given group of sides?
i) 3 cm, 4 cm, 5 cm
ii) 6 cm, 7 cm, 13 cm
iii) 3 cm, 4 cm, 1 cm
iv) 5 cm, 12 cm, 15 cm
Answer:
A triangle is possible only if the sum of the lengths of any two sides is greater than the third side.
Case (i): 3 cm, 4 cm, 5 cm
\(3 + 4 = 7 > 5\) (True)
\(3 + 5 = 8 > 4\) (True)
\(4 + 5 = 9 > 3\) (True)
Answer for (i): Possible

Case (ii): 6 cm, 7 cm, 13 cm
\(6 + 7 = 13\) (Not greater than 13)
Answer for (ii): Not possible

Case (iii): 3 cm, 4 cm, 1 cm
\(1 + 3 = 4\) (Not greater than 4)
Answer for (iii): Not possible

Case (iv): 5 cm, 12 cm, 15 cm
\(5 + 12 = 17 > 15\) (True)
\(5 + 15 = 20 > 12\) (True)
\(12 + 15 = 27 > 5\) (True)
Answer for (iv): Possible
In simple words: Check if adding the two smaller side lengths gives a sum strictly greater than the largest side length.

Exam Tip: Quick check: Just add the two smaller numbers and compare with the largest number.

Question 6. In which of the following cases is the construction of a triangle possible ?
i) \(80^\circ, 55^\circ, 45^\circ\)
ii) \(75^\circ, 86^\circ, 20^\circ\)
iii) \(90^\circ, 40^\circ, 50^\circ\)
iv) \(100^\circ, 35^\circ, 55^\circ\)
Answer:
A triangle can be constructed if and only if the sum of its three interior angles is exactly \(180^\circ\).
Case (i): \(80^\circ + 55^\circ + 45^\circ = 180^\circ\)
Answer for (i): Possible

Case (ii): \(75^\circ + 86^\circ + 20^\circ = 181^\circ \neq 180^\circ\)
Answer for (ii): Not possible

Case (iii): \(90^\circ + 40^\circ + 50^\circ = 180^\circ\)
Answer for (iii): Possible

Case (iv): \(100^\circ + 35^\circ + 55^\circ = 190^\circ \neq 180^\circ\)
Answer for (iv): Not possible
In simple words: Add the three given angles together; if the total is exactly \(180^\circ\), the triangle is possible.

Exam Tip: Always verify angle sums carefully before concluding.