# Question 1

**Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 4cm, CD = 6.5 cm, DA = 3cm and BD = 6.5 cm.**

**Solution:**

Steps of construction:

1. Draw BD = 6.5cm.

2. With B as centre and BC (=4cm) as radius draw an arc.

3. With D as centre and DC (=6.5cm) as radius draw another arc to cut the arc of step 2 at C.

4. With B as centre and BA (=4.5cm) draw an arc.

5. With D as centre and DA (=3cm) draw another arc to cut the arc of step 4 as A.

6. Join BC, CD, AB and AD.

Then, ABCD is the required quadrilateral.

# Question 2

**Construct a rhombus with side 4.5 cm and one diagonal 6 cm.**

**Solution:**

Steps of construction:

1. Draw AC = 6 cm.

2. With A as centre and 4.5cm as radius draw two arcs on either side of AC.

3. With C as centre and the same radius draw two arcs on either side of AC to cut the arcs of step 2 at B and D respectively.

4. Join AB, BC, CD and DA.

ABCD is the required rhombus.

# Question 3

**Construct a quadrilateral ABCD in which AB = 4 cm, BC = 3 cm, AD = 2.5 cm, AC = 4.5 cm and BD = 4 cm.**

**Solution:**

Steps of construction:

1. Draw AB = 4 cm.

2. With A as centre and AD (= 2.5 cm) as radius draw an arc.

3. With B as centre and BD (= 4 cm) as radius draw another arc to cut the arc of step 2 at D.

4. With A as centre and AC (= 4.5 cm) as radius draw an arc.

5. With B as centre and BC (= 3 cm) as radius draw another arc to cut the arc of step 4 at C.

6. Join AD, BC and CD.

ABCD is the required quadrilateral.

# Question 4

**Construct a quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD =10 cm.**

**Solution:**

Steps of construction:

1. Draw BC = 7.5 cm.

2. With B as centre and BD (= 10cn) draw an arc.

3. With C as centre and CD (= 5 cm) as radius draw another arc to cut the arc of step 2 at D.

4. With C as centre and CA (= 6 cm) draw an arc.

5. With D as centre and DA (= 6 cm) draw another arc to cut the arc of step 4 at A.

6. Join AB, CD and AD.

ABCD is the required quadrilateral.

# Question 5

**Construct a quadrilateral ABCD in which AB = 5.5 cm, BC = 4 cm, âˆ A = 60Â°, âˆ B = 105Â° and âˆ C = 105Â°.**

**Solution:**

Steps of construction:

1. Draw AB = 5.5 cm.

2. At A construct an angle BAAâ€™ of measure 60Â° .

3. At B, using a protractor, draw an angle ABBâ€™ of measure 105Â° .

4. With B as centre mark BC = 4 cm on BBâ€™.

5. At C, using a protractor, draw an angle BCCâ€™ of measure 105Â° .

6. CCâ€™ intersects AAâ€™ at D.

ABCD is the required quadrilateral.

# Question 6

**Construct a quadrilateral ABCD in which BC = 5.5 cm, CD = 4 cm, âˆ A = 70Â°, âˆ B = 110Â° and âˆ D = 85Â°.**

**Solution:**

C = 360Â° - (âˆ A + âˆ B + âˆ D)

Â Â Â Â Â = 360Â° - (70Â° + 110Â° + 85Â°)

Â Â Â Â Â = 360Â° - 255Â°

Â Â Â Â Â = 105Â°

Steps of construction:

1. Draw BC = 5.5 cm.

2. At B, draw an angle BCCâ€™ of measure 105Â° using a protractor.

3. With C as centre draw an arc on CCâ€™ such that CD = 4 cm.

4. At D, draw an angle of measure 85Â° using a protractor.

5. At B, draw an angle BCCâ€™ of measure 110Â° using a protractor to cut DDâ€™ at A.

ABCD is the required quadrilateral.

# Question 7

**Construct a parallelogram whose two sides and one angle are 4 cm, 5.5 cm and 700 respectively.**

**Solution:**

âˆ P = 70Â°

âˆ´ âˆ Q = 180Â° - 70Â° = 110Â°

Steps of construction:

1. Draw PQ = 4 cm.

2. At P, draw an angle QPPâ€™ of measure 70Â° .

3. With P as centre and PS (= 5.5 cm) as radius draw an arc on PPâ€™ to cut PPâ€™ at S.

4. At Q, draw an angle of PQQâ€™ of measure 110Â° .

7. With Q as centre and QR (= 5.5 cm) as radius draw an arc on QQâ€™ to cut QQâ€™ at R.

5. Join SR.

PQRS is the required parallelogram.

# Question 8

**Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4 cm, âˆ Q = 75Â° and âˆ R = 120Â°.**

**Solution:**

Steps of construction:

1. Draw QR = 2.5 cm.

2. At Q, construct an angle Q'QQ'' = 30Â° .

3. Draw QQ''' the bisector of angle Q'QQ'' to get the angle Q = 75Â°ï€®

4. Mark a point on QQ''' such that QP = 3.5 cm.

5. At R, construct an angle QRR' = 120Â°.

6. Mark a point S on RR' such that RS = 4 cm.

7. Join PS.

PQRS is the required quadrilateral.

# Question 9

**Construct a rectangle with sides 4.5 cm and 6 cm.**

**Solution:**

Steps of construction:

1. Draw AB = 6 cm.

2. At A, draw AAâ€™ perpendicular to AB.

3. With A as centre and AD (= 4.5 cm) as radius draw an arc on AAâ€™ to cut AAâ€™ at D.

4. At B, draw BBâ€™ perpendicular to AB.

5. With B as centre and BC (= 4.5 cm) as radius draw an arc on BBâ€™ to cut BBâ€™ at C.

6. Join CD.

ABCD is the required rectangle.