CBSE Class 5 Mathematics Lines And Angles Worksheet

Unit 18 : Lines, Angles and Circles & Unit 19 : Triangles

I. Fill in the blanks :

Question 1. A line segment has ______________ end points.
Answer: 2
In simple words: A line segment is bounded by two distinct fixed endpoints.

Exam Tip: Remember that a line has no endpoints, a ray has 1 endpoint, and a line segment has 2 endpoints.

Question 2. A ray extends in _____________ direction.
Answer: one
In simple words: A ray starts at one fixed point and goes on endlessly in a single direction.

Exam Tip: Rays are unidirectional geometry elements.

Question 3. A _____________ has a definite length.
Answer: line segment
In simple words: Since a line segment has two endpoints, it can be measured with a ruler.

Exam Tip: Lines and rays cannot be measured because they are infinitely long.

Question 4. A line has _____________ end points.
Answer: no / zero
In simple words: A line extends infinitely in both directions without stopping.

Exam Tip: Do not confuse a line with a line segment.

Question 5. You can not measure a __________ and a _____________.
Answer: line, ray
In simple words: Both lines and rays go on forever, so their lengths cannot be measured.

Exam Tip: Only finite figures like line segments can be measured.

Question 6. A ray has _____________ end point.
Answer: one
In simple words: The starting point of a ray is its single endpoint.

Exam Tip: Memorize the endpoint counts: Line = 0, Ray = 1, Line segment = 2.

Question 7. Two rays having a common end point form an _____________.
Answer: angle

In simple words: An angle is created when two rays share a common vertex point.

Exam Tip: The common endpoint is called the vertex of the angle.

Question 8. A right angle measures _____________.
Answer: \(90^\circ\)
In simple words: A quarter turn or perpendicular meeting forms a \(90^\circ\) right angle.

Exam Tip: Right angles are often marked with a small square at the vertex.

Question 9. Acute angles is more than _____________ and less than _____________.
Answer: \(0^\circ\), \(90^\circ\)
In simple words: Any angle smaller than a right angle is an acute angle.

Question 10. A _____________ angle measures \(180^\circ\).
Answer: straight
In simple words: A straight angle looks like a single straight line.

Exam Tip: Equivalent to two right angles (\(90^\circ \times 2 = 180^\circ\)).

Question 11. _____________ angle is more than \(90^\circ\) and less than \(180^\circ\).
Answer: Obtuse
In simple words: An obtuse angle is wider than a right angle but flatter than a straight line.

Exam Tip: "Obtuse" means blunt or wide.

Question 12. An angle that is \(89^\circ\) is an ___________ angle.
Answer: acute
In simple words: Since \(89^\circ\) is less than \(90^\circ\), it is acute.

Exam Tip: Even being \(1^\circ\) less than \(90^\circ\) makes it acute.

Question 13. _____________ angle is more than \(0^\circ\) and less than \(90^\circ\).
Answer: Acute
In simple words: The standard definition range for acute angles.

Exam Tip: Exactly \(0^\circ\) is a zero angle, not acute.

Question 14. The common end point which forms an angle is called its_____________.
Answer: vertex
In simple words: The corner point where two arms meet is the vertex.

Exam Tip: Plural of vertex is vertices.

Question 15. The part of line that has 2 end point is a _____________.
Answer: line segment
In simple words: A finite piece of a line.

Exam Tip: Essential geometric definition.

Question 16. An angle that is \(100^\circ\) is an _____________ angle.
Answer: obtuse
In simple words: Since \(100^\circ\) is greater than \(90^\circ\) and less than \(180^\circ\), it is obtuse.

Exam Tip: Check if the angle measure exceeds \(90^\circ\) to classify as obtuse.

Question 17. Lines that meet at right angle are called _____________ lines.
Answer: perpendicular
In simple words: Lines intersecting at \(90^\circ\) form perpendicular lines.

Exam Tip: The symbol for perpendicular is \(\perp\).

Question 18. The needles at 9:15 a.m. form a _____________ angle on the face of the clock.
Answer: obtuse
In simple words: At 9:15, the hour hand has moved past 9 towards 10, and the minute hand is at 3, creating an obtuse angle greater than \(90^\circ\).

Exam Tip: Visualize the clock dial: each hour interval represents \(30^\circ\).

Question 19. Every point on a circle is at the same distance from the _____________.
Answer: centre
In simple words: The center is equidistant from all points on the boundary.

Exam Tip: This fixed distance is the radius of the circle.

Question 20. A line segment from centre to any point on the circle is called _____________.
Answer: radius
In simple words: The radius connects the center to the circumference.

Exam Tip: Plural form is radii.

Question 21. All the radii of a circle are _____________.
Answer: equal in length
In simple words: Every radius in the same circle has the exact same measurement.

Question 22. A line segment whose end points are on the circle is called a _____________ of the circle.
Answer: chord
In simple words: A chord connects any two points on the boundary of a circle.

Exam Tip: The diameter is a special chord passing through the center.

Question 23. The longest chord of a circle is called a _____________.
Answer: diameter
In simple words: The diameter passes right through the center, making it the maximum possible chord length.

Exam Tip: Diameter = \(2 \times \text{Radius}\).

Question 24. The radius of circle is _____________ of the diameter.
Answer: half (\(\frac{1}{2}\))
In simple words: Radius is exactly half the length of the diameter.

Exam Tip: Formula: \(r = \frac{d}{2}\).

Question 25. The diameter of a circle is passes through the _____________ of the circle.
Answer: centre
In simple words: A chord is only a diameter if it passes through the center point.

Exam Tip: Passing through the center is mandatory for a diameter.

Question 26. The diameter of a circle is _____________ the radius.
Answer: twice / double
In simple words: Diameter is two times the radius length.

Exam Tip: Formula: \(d = 2 \times r\).

Question 27. All the diameters of a circle are _____________.
Answer: equal in length
In simple words: No matter which direction a diameter is drawn through the center, its length is constant.

Exam Tip: All diameters equal \(2r\).

Question 28. We can use a _____________ protractor to measure angles.
Answer: semi-circular / circular
In simple words: Standard geometry protractors are semi-circular instruments marked in degrees.

Exam Tip: Standard school protractors measure up to \(180^\circ\).

Question 29. In \(\triangle PQR\), the vertex is __________ and the arms are ___________ and _________.
Answer: Q, PQ, QR (or vertex depends on angle context, assuming general vertex Q or corresponding points)
In simple words: The corner point and sides forming the angle.

Exam Tip: Always identify vertex and arms relative to the specified angle.

Question 30. Diameter = 2 x ______________.
Answer: radius
In simple words: Multiply the radius by 2 to get the diameter.

Question 31. Radius = ____________ ÷ 2
Answer: Diameter
In simple words: Divide the diameter by 2 to get the radius.

Exam Tip: \(r = d \div 2\).

Question 32. The radius of a circle is 6 cm. Its diameter is ____________.
Answer: 12 cm
In simple words: Diameter = \(2 \times 6\text{ cm} = 12\text{ cm}\).

Exam Tip: Always include units in your final answer.

Question 33. The diameter of a circle is 11 cm. Its radius is ______________.
Answer: 5.5 cm
In simple words: Radius = \(11\text{ cm} \div 2 = 5.5\text{ cm}\).

Exam Tip: Half of 11 is 5.5.

Question 34. A triangle has __________ sides and _________ vertices.
Answer: 3, 3
In simple words: A triangle is a 3-sided polygon with 3 corners.

Exam Tip: "Tri" means three.

Question 35. A scalene triangles has all sides are _____________ in lengths.
Answer: unequal / different
In simple words: A scalene triangle has no equal sides.

Exam Tip: All three side lengths are distinct.

Question 36. An equilateral triangle has all sides, are ___________ in lengths.
Answer: equal
In simple words: An equilateral triangle has three equal sides and three equal angles.

Exam Tip: Each interior angle is exactly \(60^\circ\).

Question 37. An isosceles triangle has ___________ sides are equal in length.
Answer: two
In simple words: An isosceles triangle has exactly two equal sides and two equal base angles.

Question 38. Each angle of an equilateral triangle is measure ______________.
Answer: \(60^\circ\)
In simple words: Since sum of angles is \(180^\circ\) and all three are equal, \(180^\circ \div 3 = 60^\circ\).

Exam Tip: Fundamental property of equilateral triangles.

Subjective Type questions :

Question 1. Find the diameter of the circle with radius
a. 2.7 cm
b. 12.3 cm
c. 7.5 cm
d. 8 cm
Answer:
Formula: Diameter (\(d\)) = \(2 \times \text{radius } (r)\)
a. \(d = 2 \times 2.7\text{ cm} = 5.4\text{ cm}\)
b. \(d = 2 \times 12.3\text{ cm} = 24.6\text{ cm}\)
c. \(d = 2 \times 7.5\text{ cm} = 15.0\text{ cm}\) (or 15 cm)
d. \(d = 2 \times 8\text{ cm} = 16\text{ cm}\)
In simple words: Multiply each given radius by 2 to find the diameter.

Exam Tip: Show the formula \(d = 2r\) before calculating.

Question 2. Find the radius of the circle with diameter
a. 9 cm
b. 14 cm
c. 4.4 cm
d. 11.8 cm
Answer:
Formula: Radius (\(r\)) = \(\text{diameter } (d) \div 2\)
a. \(r = 9\text{ cm} \div 2 = 4.5\text{ cm}\)
b. \(r = 14\text{ cm} \div 2 = 7\text{ cm}\)
c. \(r = 4.4\text{ cm} \div 2 = 2.2\text{ cm}\)
d. \(r = 11.8\text{ cm} \div 2 = 5.9\text{ cm}\)
In simple words: Divide each given diameter by 2 to find the radius.

Exam Tip: State \(r = \frac{d}{2}\) clearly.

Question 3. Draw the circles
a. radius = 4.5 cm
b. Diameter = 10 cm
c. radius = 3.5 cm and measure its longest chord
Answer:
Construction Steps:
1. For (a), set your compass to a radius of 4.5 cm using a ruler, place the needle at center point O, and draw the circle.
2. For (b), first find radius = \(10 \div 2 = 5\text{ cm}\). Set compass to 5 cm and draw the circle.
3. For (c), draw a circle with radius 3.5 cm (diameter = 7 cm). Measure its longest chord (diameter), which will equal exactly 7 cm.
In simple words: Use a compass and ruler to draw circles according to the given measurements.

Exam Tip: Ensure the compass pencil is sharp and held firmly during rotation.

Question 4. Construct the following angels and state the type of angles.
a. \(65^\circ\)
b. \(120^\circ\)
c. \(90^\circ\)
d. \(30^\circ\)
e. \(105^\circ\)
Answer:
a. \(65^\circ\) - Acute angle
b. \(120^\circ\) - Obtuse angle
c. \(90^\circ\) - Right angle
d. \(30^\circ\) - Acute angle
e. \(105^\circ\) - Obtuse angle
In simple words: Use a protractor to draw each angle and classify based on whether it is less than, equal to, or greater than \(90^\circ\).

Exam Tip: Always label the arms and vertex of constructed angles.

Question 5. In \(\triangle ABC\), \(\angle A = 50^\circ\) and \(\angle B = 70^\circ\), then find \(\angle C = ?\)
Answer:
Sum of interior angles of a triangle = \(180^\circ\)
\(\angle A + \angle B + \angle C = 180^\circ\)
\(50^\circ + 70^\circ + \angle C = 180^\circ\)
\(120^\circ + \angle C = 180^\circ\)
\(\angle C = 180^\circ - 120^\circ = 60^\circ\)
In simple words: Subtract the sum of the two given angles from \(180^\circ\) to find the third angle.

Exam Tip: Angle sum property of triangles is essential for such problems.

Question 6. In an isosceles \(\triangle PQR\), \(\angle P = \angle R = 65^\circ\), then find \(\angle Q = ?\)
Answer:
Sum of interior angles of a triangle = \(180^\circ\)
\(\angle P + \angle Q + \angle R = 180^\circ\)
\(65^\circ + \angle Q + 65^\circ = 180^\circ\)
\(130^\circ + \angle Q = 180^\circ\)
\(\angle Q = 180^\circ - 130^\circ = 50^\circ\)
In simple words: Add the two equal angles and subtract from \(180^\circ\) to find \(\angle Q\).

Exam Tip: In an isosceles triangle, angles opposite to equal sides are equal.

Question 7. Measure the following angles and state the type of angle.
(Based on the figures: X-Y-Z, P-Q-R, A-B-C)
Answer:
1. Angle XYZ: Measured using protractor (approx. \(120^\circ\) to \(135^\circ\)) - Obtuse angle
2. Angle PQR: Measured using protractor (approx. \(45^\circ\) to \(60^\circ\)) - Acute angle
3. Angle ABC: Measured using protractor (approx. \(70^\circ\) to \(80^\circ\)) - Acute angle
In simple words: Place protractor center at the vertex and read the degree measure, then classify.

Exam Tip: Align the baseline of the protractor accurately along one arm of the angle.

Question 8. With the help of the figure, write the name of the following
i) PQ =
ii) AB =
iii) O =
iv) OC =
Answer:
i) PQ = Chord (or arc/chord segment depending on diagram context)
ii) AB = Diameter
iii) O = Centre of the circle
iv) OC = Radius
In simple words: Identify the geometric parts of the circle labeled in the figure.

Exam Tip: Review circle terminology carefully.

Question 9. In the given figure name the following
i) Centre of the circle
ii) All the radii
iii) All the diameters
iv) All the chords
Answer:
i) Centre of the circle: O
ii) All the radii: OA, OB, OC, OE (or O to respective boundary points)
iii) All the diameters: AB (or EF passing through center O)
iv) All the chords: AB, EF, CD (any line segment joining two points on the circle)
In simple words: Read the labels from the circle diagram to list center, radii, diameters, and chords.

Question 10. In which of the following cases is a triangle possible with given group of sides
i) 8 cm, 7 cm, 15 cm
ii) 9 cm, 6 cm, 8 cm
iii) 1 cm, 2 cm, 4 cm
iv) 3 cm, 4 cm, 5 cm
Answer:
Triangle Inequality Theorem: The sum of any two sides must be strictly greater than the third side.
i) \(8 + 7 = 15\) (Not greater than 15) - Not possible
ii) \(6 + 8 = 14 > 9\) - Possible
iii) \(1 + 2 = 3\) (Not greater than 4) - Not possible
iv) \(3 + 4 = 7 > 5\) - Possible
In simple words: A triangle is possible only when the sum of the two smaller sides is greater than the longest side.

Exam Tip: Always check the sum of the two shorter sides first.

Question 11. In which of the following cases is the construction of a triangle possible.
i) \(80^\circ, 70^\circ, 60^\circ\)
ii) \(90^\circ, 45^\circ, 45^\circ\)
iii) \(50^\circ, 50^\circ, 80^\circ\)
iv) \(39^\circ, 85^\circ, 65^\circ\)
Answer:
Angle Sum Property: The sum of the three interior angles of a triangle must be exactly \(180^\circ\).
i) \(80^\circ + 70^\circ + 60^\circ = 210^\circ \neq 180^\circ\) - Not possible
ii) \(90^\circ + 45^\circ + 45^\circ = 180^\circ\) - Possible
iii) \(50^\circ + 50^\circ + 80^\circ = 180^\circ\) - Possible
iv) \(39^\circ + 85^\circ + 65^\circ = 189^\circ \neq 180^\circ\) - Not possible
In simple words: Add the three given angles. If the sum equals \(180^\circ\), the triangle is possible.

Exam Tip: Always verify that angle sums total exactly \(180^\circ\).