CBSE Class 8 Mathematics Practical Geometry Worksheet Set 05

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Question 1. To construct a quadrilateral uniquely the number of parts to know are:
(A) 2
(B) 3
(C) 4
(D) 5
Answer: (D) 5
A quadrilateral is uniquely determined when the measures of 5 independent elements (sides, diagonals, or angles) are known.
In simple words: You need 5 measurements to draw a unique quadrilateral.

Exam Tip: Remember that five independent measurements are always required to construct a unique quadrilateral.

Question 2. Construction of a square is possible when one side PQ of square PQRS is given, because
(A) All sides are equal
(B) Each angles is 90\(^\circ\) and all sides are equal.
(C) It is a rhombus
(D) None
Answer: (B) Each angles is 90\(^\circ\) and all sides are equal.
A square has all four sides equal and all four interior angles equal to 90\(^\circ\). Thus, knowing just one side gives us all side lengths and angle measures implicitly.
In simple words: All sides of a square are equal and its corners are right angles, so one side is enough.

Exam Tip: Special quadrilaterals like squares and rhombuses require fewer than 5 explicit measurements because their special properties supply the rest.

Question 3. It is possible to construct a rhombs ABCD with two measurements AC = 6cm and BD = 8cm because
(A) Diagonals of a rhombus are perpendicular bisectors of one another
(B) Four sides are equal
(C) Each angle is 90\(^\circ\)
(D) Diagonal bisect each other
Answer: (A) Diagonals of a rhombus are perpendicular bisectors of one another
Since the diagonals of a rhombus bisect each other at right angles, we can construct the perpendicular axes of lengths 6 cm and 8 cm and join their endpoints to form the rhombus.
In simple words: The two diagonals intersect at 90 degrees and cut each other in half, which is enough to draw the rhombus.

Exam Tip: A rhombus can be uniquely constructed if its two diagonals are given.

Question 4. A quadrilateral PQRS cannot be constructed with measurement PQ = 6 cm, QR = 9.5 cm
(A) Angle sum property of quadrilateral
(B) Data not enough
(C) All sides are not given
(D) None
Answer: (B) Data not enough
To construct a unique quadrilateral, 5 independent measurements are required. Here, only 2 measurements are provided, which is insufficient.
In simple words: Only two side lengths are given, but we need five pieces of information.

Exam Tip: Always count the given parameters. If fewer than 5 independent measurements are provided for a general quadrilateral, the data is insufficient.

Question 5. A quadrilateral ABCD cannot be drawn with the measurements AB = 3cm, BC = 4cm, CD = 4.5 cm, DA = 2cm and BD = 6cm because
(A) Data not enough
(B) AB + DA < BD
(C) BC + CD > BD
(D) None
Answer: (B) AB + DA < BD
In triangle ABD, the sum of lengths of two sides must be strictly greater than the third side. Here, AB = 3 cm and DA = 2 cm, so \(AB + DA = 3 + 2 = 5\) cm, which is less than BD = 6 cm. This violates the triangle inequality theorem.
In simple words: The sum of two sides (3 cm + 2 cm) is less than the third side (6 cm), which is impossible for a triangle.

Exam Tip: Always check the triangle inequality condition (\(a + b > c\)) for any triangles formed by sides and diagonals before construction.

Question 6. Sum of the angles of a quadrilateral is
(A) 270\(^\circ$
(B) 360\(^\circ$
(C) 90\(^\circ$
(D) 180\(^\circ$
Answer: (B) 360\(^\circ$
The sum of all four interior angles of any quadrilateral is always equal to 360\(^\circ\).
In simple words: All four interior angles of a quadrilateral always add up to 360 degrees.

Question 7. A quadrilateral has total number of elements as
(A) Four
(B) Five
(C) Six
(D) Ten
Answer: (D) Ten
A quadrilateral has 10 elements in total: 4 sides, 4 angles, and 2 diagonals.
In simple words: A quadrilateral has 4 sides, 4 angles, and 2 diagonals, making 10 parts in total.

Exam Tip: Elements of a polygon include its sides, angles, and diagonals.

Question 8. If the measure of each angle is less than 180\(^\circ\), the quadrilateral is known as:
(A) Concave figure
(B) Parallelogram
(C) Convex quadrilateral
(D) None
Answer: (C) Convex quadrilateral
A polygon in which each interior angle is strictly less than 180\(^\circ\) is called a convex polygon.
In simple words: When all interior angles are less than 180 degrees, it is a convex quadrilateral.

Exam Tip: In a convex quadrilateral, both diagonals lie entirely inside the figure.

Question 9. A quadrilateral having all sides equal and one angle measuring 90\(^\circ\) is called.
(A) Square
(B) Kite
(C) Trapezium
(D) None
Answer: (A) Square
A rhombus with one interior angle equal to 90\(^\circ\) is a square.
In simple words: Equal sides and a right angle make it a square.

Exam Tip: A rhombus has equal sides, but if one angle is 90 degrees, all angles become 90 degrees, turning it into a square.

Question 10. A quadrilateral having two pairs of equal adjacent sides and unequal opposite sides is called.
(A) Parallelogram
(B) Rectangle
(C) Square
(D) Kite
Answer: (D) Kite
A kite is defined as a quadrilateral with two distinct pairs of adjacent sides that are equal in length.
In simple words: A kite has two pairs of equal sides next to each other.

Exam Tip: Memorize the definitions of special quadrilaterals: kite, rhombus, parallelogram, trapezium, rectangle, and square.

Question 11. We Draw a rough sketch of the quadrilateral and indicate the measurement because
(A) Original cannot be drawn
(B) It is always convenient and helpful.
(C) Not necessary
(D) None
Answer: (B) It is always convenient and helpful.
A rough sketch helps visualize the given measurements and plan the steps of construction accurately.
In simple words: A rough sketch helps us plan how to construct the figure step by step.

Exam Tip: Always make a rough labeled diagram before starting any geometric construction.

Question 12. To construct a parallelogram if the adjacent sides are given, still there is a need for measurement of
(A) Angles
(B) Other two sides
(C) Diagonal
(D) None
Answer: (A) Angles
Knowing adjacent sides gives two sides, and opposite sides are equal in a parallelogram, giving four side lengths. To fix the shape, we need the included angle between the adjacent sides.
In simple words: We need an angle between the sides to fix the shape of the parallelogram.

Exam Tip: A parallelogram requires either two adjacent sides and an included angle, or two adjacent sides and a diagonal.

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Question 13. Four sides of a Quadrilateral ABCD as AB = 4cm, BC = 6cm, CD = 5.5cm, AD = 5 cm and one diagonal AC = 8 cm. Construct a quadrilateral.
Answer:
1. Draw a line segment AC = 8 cm.
2. With A as center and radius 5 cm, draw an arc.
3. With C as center and radius 6 cm, draw another arc intersecting the previous arc at B.
4. Join AB and BC.
5. With A as center and radius 5 cm, draw an arc on the other side of AC.
6. With C as center and radius 5.5 cm, draw an arc intersecting this arc at D.
7. Join AD and CD. ABCD is the required quadrilateral.
In simple words: Construct two triangles (ABC and ADC) sharing the common diagonal AC.

Exam Tip: When four sides and one diagonal are given, draw the triangle with the diagonal first.

Question 14. Construct a Quadrilateral HOPE in which HO = 4.5cm, OP = 4cm, PE = 6.5 cm, EH = 3cm and OE = 6.5 cm.
Answer:
1. Draw diagonal OE = 6.5 cm.
2. With center O and radius 4 cm, draw an arc.
3. With center E and radius 6.5 cm, draw an arc intersecting at P.
4. Join OP and EP.
5. With center O and radius 4.5 cm, draw an arc on the other side of OE.
6. With center E and radius 3 cm, draw an arc intersecting at H.
7. Join OH and EH. HOPE is the required quadrilateral.
In simple words: Draw the diagonal OE first, then construct triangles OPE and OHE on opposite sides.

Exam Tip: Double check the compass radius settings carefully for accuracy.

Question 15. Construct a Quadrilateral ABCD in which AB = 5 cm, BC = 4cm, \(\angle A = 60^\circ\), \(\angle B = 105^\circ\) and \(\angle C = 105^\circ\).
Answer:
1. Draw line segment AB = 5 cm.
2. At point B, construct an angle of \(105^\circ\).
3. Along the ray from B, cut off BC = 4 cm.
4. At point C, construct an angle of \(105^\circ\).
5. At point A, construct an angle of \(60^\circ\) such that its ray intersects the ray from C at point D.
6. ABCD is the required quadrilateral.
In simple words: Draw side AB, make angles at A and B, mark BC, make angle at C, and close the shape at D.

Exam Tip: Use a protractor or compass constructions for standard angles like \(60^\circ\), \(105^\circ\).

Question 16. Construct a Quadrilateral PQRS in which PQ = 4cm, QR = 3cm, PS = 2.5cm, PR = 4.5cm and QS = 4cm
Answer:
1. Draw PQ = 4 cm.
2. With P as center and radius 2.5 cm, draw an arc.
3. With Q as center and radius 4 cm (diagonal QS), draw an arc intersecting at S.
4. Join PS and QS.
5. With Q as center and radius 3 cm, draw an arc.
6. With P as center and radius 4.5 cm (diagonal PR), draw an arc intersecting at R.
7. Join QR, SR, and PR. PQRS is the required quadrilateral.
In simple words: Construct triangle PQS first, then locate vertex R using diagonals and remaining side.

Exam Tip: When two diagonals and three sides are given, identify the triangle whose three side lengths are fully known.

Question 17. Construct a Rhombus with side 4.5 cm and one diagonal 6 cm.
Answer:
1. Draw diagonal AC = 6 cm.
2. With A as center and radius 4.5 cm, draw arcs above and below AC.
3. With C as center and radius 4.5 cm, draw arcs above and below AC intersecting previous arcs at B and D.
4. Join AB, BC, CD, and DA. ABCD is the required rhombus.
In simple words: Draw the diagonal, then use the equal side length to strike intersecting arcs from both ends.

Exam Tip: All four sides of a rhombus are equal in length.

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Question 18. Construct a Quadrilateral PQRS where PQ = 4cm, QR = 6cm, RS = 5cm, PS = 5.5 cm and PR = 7cm.
Answer:
1. Draw diagonal PR = 7 cm.
2. With P as center and radius 4 cm, draw an arc.
3. With R as center and radius 6 cm, draw an arc intersecting at Q.
4. Join PQ and RQ.
5. With P as center and radius 5.5 cm, draw an arc on the other side of PR.
6. With R as center and radius 5 cm, draw an arc intersecting at S.
7. Join PS and RS. PQRS is the required quadrilateral.
In simple words: Draw diagonal PR, construct triangle PQR on one side and triangle PSR on the other side.

Exam Tip: Clearly label all vertices and measurements on the final construction.

Question 19. Construct Quadrilateral ABCD in which AB = 4.5 cm, BC = 3.5cm, CD = 5cm, \(\angle B = 45^\circ\) and \(\angle C = 150^\circ\).
Answer:
1. Draw line segment BC = 3.5 cm.
2. At B, construct an angle of \(45^\circ\).
3. Along this ray, cut off AB = 4.5 cm.
4. At C, construct an angle of \(150^\circ\).
5. Along this ray, cut off CD = 5 cm.
6. Join AD. ABCD is the required quadrilateral.
In simple words: Start with side BC, build angles at B and C, mark off AB and CD, then join AD.

Exam Tip: Construct \(150^\circ\) by combining \(90^\circ\) and \(60^\circ\) or using a protractor accurately.

Question 20. Construct a quadrilateral ABCD in which AB = 6cm, BC = 5 cm, \(\angle A = 55^\circ\), \(\angle B = 110^\circ\) and \(\angle D = 90^\circ\).
Answer:
1. Calculate the fourth angle \(\angle C\): Sum of angles = \(360^\circ\).
\(\angle C = 360^\circ - (55^\circ + 110^\circ + 90^\circ) = 360^\circ - 255^\circ = 105^\circ\).
2. Draw AB = 6 cm.
3. At B, construct \(\angle B = 110^\circ\) and cut off BC = 5 cm.
4. At C, construct \(\angle C = 105^\circ\).
5. At A, construct \(\angle A = 55^\circ\) such that its ray intersects the ray from C at D.
6. ABCD is the required quadrilateral.
In simple words: Find the missing angle C using the angle sum property first, then proceed with side and angle constructions.

Exam Tip: Always find all possible interior angles using the 360-degree sum property before starting construction if an angle is missing.

Question 21. Construct a Quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6cm, CD = 5 cm and BD = 10 cm.
Answer:
1. Draw BC = 7.5 cm.
2. With B as center and radius 10 cm, draw an arc.
3. With C as center and radius 5 cm, draw an arc intersecting at D.
4. Join BD and CD.
5. With C as center and radius 6 cm, draw an arc.
6. With D as center and radius 6 cm, draw an arc intersecting at A.
7. Join AC, AD, and AB. ABCD is the required quadrilateral.
In simple words: Construct triangle BCD first, then locate vertex A using distances from C and D.

Exam Tip: Verify triangle side lengths before drawing intersecting arcs.

Question 22. Construct a Parallelogram ABCD with AB = 3.5 cm, BC = 4 cm and AC = 6.5 cm.
Answer:
1. Draw triangle ABC with AB = 3.5 cm, BC = 4 cm, and AC = 6.5 cm.
2. With A as center and radius equal to BC (4 cm), draw an arc opposite to C.
3. With C as center and radius equal to AB (3.5 cm), draw an arc intersecting at D.
4. Join AD and CD. ABCD is the required parallelogram.
In simple words: Construct triangle ABC, then use opposite sides to complete the parallelogram.

Exam Tip: Opposite sides of a parallelogram are equal in length (\(AD = BC\) and \(CD = AB\)).

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Question 23. Construct a Quadrilateral ABCD in which AB = AD = 5cm, CD = 5.5cm, \(\angle A = 90^\circ\) and \(\angle D = 120^\circ\).
Answer:
1. Draw AB = 5 cm.
2. At A, construct an angle \(\angle A = 90^\circ\).
3. Along this ray, cut off AD = 5 cm.
4. At D, construct an angle \(\angle D = 120^\circ\).
5. Along this ray, cut off DC = 5.5 cm.
6. Join BC. ABCD is the required quadrilateral.
In simple words: Draw side AB, construct 90 degree angle at A to mark AD, construct 120 degree angle at D to mark DC, then join B to C.

Exam Tip: Construct \(120^\circ\) by drawing an arc of radius and marking two successive \(60^\circ\) steps on it.

Question 24. Construct a Square with one side 5.1 cm.
Answer:
1. Draw line segment AB = 5.1 cm.
2. At points A and B, construct \(90^\circ\) angles using a compass or protractor.
3. With A and B as centers and radius 5.1 cm, draw arcs on these perpendicular rays to mark points D and C respectively.
4. Join DC. ABCD is the required square.
In simple words: Draw a base side, erect 90 degree perpendiculars at both ends of length 5.1 cm, and connect the top ends.

Exam Tip: All sides of a square are equal and all interior angles are \(90^\circ\).

Question 25. Construct a rectangle with sides 4.5 cm and 6 cm.
Answer:
1. Draw base AB = 6 cm.
2. At A and B, construct \(90^\circ\) angles.
3. With center A and radius 4.5 cm, cut an arc on the perpendicular at A to mark point D.
4. With center B and radius 4.5 cm, cut an arc on the perpendicular at B to mark point C.
5. Join DC. ABCD is the required rectangle.
In simple words: Draw the longer side as base, erect right angles at both ends, cut off height 4.5 cm, and join the top.

Exam Tip: Opposite sides of a rectangle are equal and all angles are \(90^\circ\).

Question 26. Construct a trapezium ABCD in which \(AB \parallel CD\), AB = 8 cm, BC = 6 cm, CD = 4 cm, and \(\angle B = 60^\circ\).
Answer:
1. Draw line segment AB = 8 cm.
2. At point B, construct \(\angle B = 60^\circ\).
3. Along this ray, cut off BC = 6 cm.
4. Through C, draw a line parallel to AB.
5. From C, cut off CD = 4 cm along the parallel line (or use intersecting arcs knowing parallel properties).
6. Join AD. ABCD is the required trapezium.
In simple words: Draw base AB, make \(60^\circ\) at B to get side BC, draw a parallel line from C of length 4 cm, and complete the trapezium.

Exam Tip: Ensure the top and bottom bases (\(AB\) and \(CD\)) are strictly parallel.