CBSE Class 8 Mathematics Practical Geometry Worksheet Set 03

Question 1. Construct a quadrilateral ABCD in which AB = 4.4cm, BC = 4cm, CD = 6.4cm, DA = 2.8cm and BD = 6.6cm
Answer:
To construct the quadrilateral ABCD:
1. Draw a line segment BD = 6.6 cm.
2. With B as the center and radius equal to 4.4 cm, draw an arc on one side of BD.
3. With D as the center and radius equal to 2.8 cm, draw another arc to intersect the previous arc at point A.
4. Join AB and AD.
5. With B as the center and radius equal to 4 cm, draw an arc on the other side of BD.
6. With D as the center and radius equal to 6.4 cm, draw another arc to intersect this arc at point C.
7. Join BC and DC.
ABCD is the required quadrilateral.
In simple words: Construct two adjacent triangles ABD and CBD sharing the common diagonal BD.

Exam Tip: Always make a rough sketch first to decide which diagonal to draw as the base.

Question 2. Construct a parallelogram ABCD where AB = 3.6cm, BC = 4.2cm and AC = 6.5cm.
Answer:
To construct the parallelogram ABCD:
1. Draw a line segment AB = 3.6 cm.
2. With A as the center and radius 6.5 cm, draw an arc.
3. With B as the center and radius 4.2 cm, draw an arc intersecting the first arc at point C.
4. Join AC and BC.
5. With A as the center and radius 4.2 cm, draw an arc opposite to BC.
6. With C as the center and radius 3.6 cm, draw an arc intersecting the previous arc at point D.
7. Join AD and CD.
ABCD is the required parallelogram.
In simple words: Draw triangle ABC first, then use opposite side lengths to locate vertex D.

Exam Tip: Remember opposite sides of a parallelogram are equal in length, so CD = AB = 3.6 cm and AD = BC = 4.2 cm.

Question 3. Construct a rhombus with side 6cm and one diagonal 8cm. Measure the other diagonal.
Answer:
To construct the rhombus:
1. Draw a line segment AC = 8 cm (first diagonal).
2. With A and C as centers and radius equal to 6 cm, draw arcs above and below AC intersecting each other at points B and D.
3. Join AB, BC, CD, and DA.
4. Measure the other diagonal BD, which is approximately 8.9 cm.
In simple words: Construct two isosceles triangles on the same base (diagonal) with equal side lengths of 6 cm.

Exam Tip: All four sides of a rhombus are equal, so use the side length as the radius for drawing arcs from the endpoints of the diagonal.

Question 4. Construct a quadrilateral ABCD in which AB = 5.5cm, AD = 4.4cm, CD = 6.5cm, AC = 6.5cm and BD = 7.1cm.
Answer:
To construct the quadrilateral ABCD:
1. Draw a line segment AB = 5.5 cm.
2. With A as the center and radius 6.5 cm (AC), draw an arc.
3. With B as the center and radius 7.1 cm (BD), this information gives us both diagonals. Alternatively, use triangle ABD first: draw AD = 4.4 cm from A, and using BD = 7.1 cm and AB = 5.5 cm, construct triangle ABD.
4. From A, draw an arc of radius 6.5 cm (AC), and from D, draw an arc of radius 6.5 cm (CD) to locate point C.
5. Join AC, BC, CD, and complete the quadrilateral.
In simple words: Build triangle ABD first, then use the lengths of AC and CD to locate point C.

Exam Tip: Check that all given side and diagonal lengths satisfy the triangle inequality theorem before finalizing vertices.

Question 5. Construct a rhombus COLD in which CL = 7.5cm, OD = 6cm
Answer:
To construct the rhombus COLD using its diagonals:
1. Draw a diagonal CL = 7.5 cm.
2. Draw the perpendicular bisector of CL intersecting it at point O' (midpoint).
3. With O' as the center, cut arcs of length \(\frac{6}{2} = 3\) cm upwards and downwards along the perpendicular bisector to get points D and O such that OD = 6 cm.
4. Join CD, LD, CO, and LO.
COLD is the required rhombus.
In simple words: Draw one diagonal, find its midpoint, and draw perpendicular arcs for half the length of the second diagonal on both sides.

Exam Tip: Diagonals of a rhombus bisect each other at right angles (90 degrees).

Question 6. Construct a rectangle PURE in which PU = 5.5cm, UR = 4cm
Answer:
To construct the rectangle PURE:
1. Draw a line segment PU = 5.5 cm.
2. At points P and U, construct angles of \(90^\circ\) using a compass or set square.
3. With U as the center and radius 4 cm, draw an arc intersecting the perpendicular line at R.
4. With P as the center and radius 4 cm, draw an arc intersecting the perpendicular line at E.
5. Join RE.
PURE is the required rectangle.
In simple words: Draw the base, erect \(90^\circ\) angles at both ends, cut off the breadth, and join the top.

Exam Tip: Opposite sides of a rectangle are equal, so PE = UR = 4 cm.

Question 7. Construct a parallelogram HARD in which HA = 7cm, AR = 5cm, \(\angle D = 105^\circ\).
Answer:
To construct the parallelogram HARD:
1. Draw a line segment HA = 7 cm.
2. Since opposite angles are equal and adjacent angles are supplementary, \(\angle A = 180^\circ - 105^\circ = 75^\circ\).
3. At point A, construct an angle of \(75^\circ\).
4. With A as the center and radius AR = 5 cm, draw an arc on the ray to locate point R.
5. At R, construct an angle of \(105^\circ\) (or use parallel lines), and cut an arc RD = 7 cm.
6. Join D to H.
HARD is the required parallelogram.
In simple words: Find angle A using adjacent angles property (\(180^\circ - 105^\circ = 75^\circ\)), draw the side, and complete the parallelogram.

Exam Tip: Consecutive angles in a parallelogram always add up to \(180^\circ\).

Question 8. Construct a quadrilateral BIRD where BI = 3.5cm, IR = 6.5cm, \(\angle B = 75^\circ\), \(\angle I = 105^\circ\) and \(\angle R = 120^\circ\).
Answer:
To construct the quadrilateral BIRD:
1. Draw a line segment BI = 3.5 cm.
2. At point I, construct an angle of \(105^\circ\).
3. With I as the center and radius IR = 6.5 cm, draw an arc on this ray to locate point R.
4. At point R, construct an angle of \(120^\circ\).
5. At point B, construct an angle of \(75^\circ\), extending the ray until it intersects the ray from R at point D.
BIRD is the required quadrilateral.
In simple words: Draw the base BI, construct the given angles at B and I, locate R along I, and find D where the rays intersect.

Exam Tip: Ensure your protractor or compass constructions for angles like \(75^\circ\) (\(60^\circ + 15^\circ\)), \(105^\circ\) (\(90^\circ + 15^\circ\)), and \(120^\circ\) are accurate.

Question 9. Construct a quadrilateral PQRS, in which \(\angle Q = 45^\circ\), \(\angle R = 90^\circ\), QR = 5cm, PQ = 9cm and RS = 7cm.
Answer:
To construct the quadrilateral PQRS:
1. Draw a line segment QR = 5 cm.
2. At point Q, construct an angle of \(45^\circ\).
3. With Q as the center and radius PQ = 9 cm, draw an arc on the ray to locate point P.
4. At point R, construct an angle of \(90^\circ\).
5. With R as the center and radius RS = 7 cm, draw an arc on the perpendicular ray to locate point S.
6. Join P to S.
PQRS is the required quadrilateral.
In simple words: Draw the base QR, construct angles at Q and R, mark off PQ and RS, and join PS.

Exam Tip: A \(45^\circ\) angle is constructed by bisecting a \(90^\circ\) angle.

Question 10. Construct a kite SOLD if OD = 8cm, SD = 5cm and LD = 6cm . Which properties of the kite did you use in the process.
Answer:
To construct the kite SOLD:
1. Draw a diagonal or use adjacent sides: In a kite, two pairs of adjacent sides are equal. Let SD = 5 cm and LD = 6 cm. Since D is a common vertex, SD = SO = 5 cm and LD = LE = 6 cm (letting OD be the axis of symmetry, wait - let us use standard notation: OD = 8 cm, SD = 5 cm, LD = 6 cm).
2. Draw OD = 8 cm.
3. With D as the center, draw arcs of radius 5 cm and 6 cm on both sides to locate points S and L.
4. Complete the kite by joining OS, SL, LD, and DO.
Properties used: In a kite, two pairs of adjacent sides are equal in length (\(\text{SD} = \text{SO}\) and \(\text{LD} = \text{LE}\)), and the diagonals intersect at right angles.
In simple words: Use the property that adjacent sides of a kite are equal to construct the upper and lower triangles symmetrically across the diagonal.

Exam Tip: State clearly which sides are equal by the definition of a kite.

Question 11. How will you construct a rectangle PLOT if you know only the lengths PL and LO?
Answer:
To construct the rectangle PLOT with only lengths PL and LO given:
1. Draw a line segment PL = given length.
2. At points P and L, construct perpendiculars of \(90^\circ\).
3. With L as the center and radius equal to LO, cut an arc on the perpendicular at L to locate point O.
4. With P as the center and radius equal to LO (since opposite sides of a rectangle are equal, PT = LO), cut an arc on the perpendicular at P to locate point T.
5. Join T to O.
In simple words: Use the rectangle property that opposite sides are equal and all interior angles are \(90^\circ\) to find the remaining dimensions.

Exam Tip: Mention that a rectangle is uniquely determined if two adjacent sides are known because the interior angles are fixed at \(90^\circ\).

Question 12. Construct a square GOAT with GO = 4.9cm
Answer:
To construct the square GOAT:
1. Draw a line segment GO = 4.9 cm.
2. At points G and O, construct perpendiculars of \(90^\circ\).
3. With G and O as centers, draw arcs of radius 4.9 cm along the perpendicular rays to locate points T and A respectively (since all sides of a square are equal, GT = OA = GO = 4.9 cm).
4. Join T to A.
GOAT is the required square.
In simple words: Draw a base, construct \(90^\circ\) angles at both ends, mark off equal side lengths of 4.9 cm, and close the top.

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

Question 13. Construct a rhombus in which the diagonals are 6.6cm and 4.8cm long.
Answer:
To construct the rhombus:
1. Draw a line segment (first diagonal) of length 6.6 cm, let us call it AC.
2. Construct the perpendicular bisector of AC, intersecting it at O.
3. From the midpoint O, measure and cut arcs of length \(\frac{4.8}{2} = 2.4\) cm upwards and downwards along the perpendicular bisector to mark the endpoints of the second diagonal, let us call them B and D.
4. Join AB, BC, CD, and DA.
The required rhombus is constructed.
In simple words: Draw one diagonal, find its midpoint, and draw perpendicular segments of half the length of the second diagonal on both sides.

Exam Tip: Diagonals of a rhombus bisect each other perpendicularly.

Question 14. Construct a square ABCD, given that diagonal AC = 6cm.
Answer:
To construct the square ABCD:
1. Draw a line segment AC = 6 cm (diagonal).
2. Construct the perpendicular bisector of AC, intersecting AC at O (midpoint).
3. Since diagonals of a square are equal and bisect each other at \(90^\circ\), the other diagonal BD also has length 6 cm and passes through O.
4. From O, measure and cut arcs of length \(\frac{6}{2} = 3\) cm along the perpendicular bisector in both directions to locate points B and D.
5. Join AB, BC, CD, and DA.
ABCD is the required square.
In simple words: Draw the diagonal, construct its perpendicular bisector, mark half-diagonal lengths (\(3\) cm) above and below, and join the vertices.

Exam Tip: Diagonals of a square are equal in length and perpendicular bisectors of each other.

Question 15. Construct a parallelogram CARE where CA = 3.9cm and AR = 5.5cm.
Answer:
To construct the parallelogram CARE:
1. Draw a line segment CA = 3.9 cm.
2. At point A, construct any convenient angle (e.g., \(60^\circ\) or \(75^\circ\)).
3. With A as the center and radius AR = 5.5 cm, draw an arc on the ray to locate point R.
4. With R as the center and radius equal to CA (3.9 cm), draw an arc.
5. With C as the center and radius equal to AR (5.5 cm), draw an arc intersecting the previous arc at point E.
6. Join RE and CE.
CARE is the required parallelogram.
In simple words: Construct an adjacent side and angle at A, then use opposite side lengths to complete the parallelogram.

Exam Tip: Opposite sides of a parallelogram are equal (\(\text{CE} = \text{AR} = 5.5\) cm and \(\text{RE} = \text{CA} = 3.9\) cm).

Question 16. Construct a rectangle with adjacent lengths 3.5cm and 4.5cm
Answer:
To construct the rectangle:
1. Draw a line segment of length 4.5 cm (base).
2. At both endpoints of the base, construct perpendicular angles of \(90^\circ\).
3. Cut off arcs of length 3.5 cm along both perpendiculars.
4. Join the top endpoints with a straight line segment.
The required rectangle is constructed.
In simple words: Draw the base, erect \(90^\circ\) angles at both ends, mark the height of 3.5 cm, and connect them.

Exam Tip: All four interior angles of a rectangle are \(90^\circ\).

Question 17. Construct a rhombus ABCD, with side AB = 7.3cm and \(\angle A = 75^\circ\)
Answer:
To construct the rhombus ABCD:
1. Draw a line segment AB = 7.3 cm.
2. At point A, construct an angle of \(75^\circ\).
3. With A as the center and radius 7.3 cm, draw an arc on the ray to locate point D (since all sides of a rhombus are equal, AD = AB = 7.3 cm).
4. With D as the center and radius 7.3 cm, draw an arc.
5. With B as the center and radius 7.3 cm, draw an arc intersecting the previous arc at point C.
6. Join DC and BC.
ABCD is the required rhombus.
In simple words: Draw side AB, construct \(75^\circ\) at A, mark off side length 7.3 cm for AD, and use compass arcs from B and D to locate C.

Exam Tip: A rhombus has all four sides equal in length.