3 Sides, 2 Diagonals

Q.

A quadrilateral can be constructed uniquely if its three sides and __________ angles are given.

Q.

When we start constructing a quadrilateral whose 2 diagonals and 3 sides known, in how many ways can the construction be started.

1. 2

2. 1

3. 3

4. 4

Q. The construction of the following quadrilateral is possible when _______ is / are given.

1. 4 sides and 1 diagonal
2. 2 sides and 1 angle
3. 5 sides of the quadrilateral
4. 3 sides and 2 diagonals

Q.

Construct the following quadrilaterals.

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

(ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Q. The construction of the following quadrilateral is possible when _______ is / are given.

1. 4 sides and 1 diagonal
2. 2 sides and 1 angle
3. 5 sides of the quadrilateral
4. 3 sides and 2 diagonals

Q.

Construct the following quadrilaterals,

(i) Quadrilateral DEAR

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

(ii) Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

∠R = 75°

∠U = 120°

Q. The construction of the following quadrilateral is possible when _______ is / are given.

1. 3 sides and 2 diagonals
2. 4 sides and 1 diagonal
3. 2 sides and 1 angle
4. 5 sides of the quadrilateral

Q. Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why? [2 marks]

Q. Girish constructed a quadrilateral PQRS, where sides PS = 5cm, SR = 3 cm, and QR = 3.5 cm, diagonals PR = 5cm and QS = 8 cm. Following is the steps of construction.

Step 1: Draw a line segment PR of length 5 cm.

Step 2: With P as center, draw an arc of radius 5 cm and R as center, draw an arc of radius 3 cm.

Step 3: Mark the intersecting point of the arcs to be S and join S to P and R.

Find the next step.

1. Quadrilateral PQRS is hence constructed.
2. Similarly from R, draw an arc of radius 3.5 cm. Mark the intersecting point to be Q.
3. Join Q to P and R.
4. To the opposite side of PR, keeping S as the center, draw an arc of radius 8 cm.

Q. Steps for the construction of a quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.5 cm, AD= 5 cm and AC = 8 cm is given below.

Choose the correct order.

1. Draw a line segment AC of 8 cm.

2. With 4 cm as radius from A draw an arc.

3. With 5 cm as radius from A draw an arc to the opposite side of AC.

4. With 6 cm as radius cut the arc drawn in step 2. Let that point of intersection be B. Join AB and CB.

5. From C take 5.5 cm as radius and cut the arc drawn in step 4. Let the point of intersection be D. Join AD and CD.

1. 1, 2, 4, 3, 5
2. 1, 2, 3, 4, 5
3. 1, 2, 5, 4, 3
4. 1, 2, 3, 5, 4

Q. Match the following elements according to the measurements required for the construction of quadrilaterals.

1. 2 diagonals
2. 1 diagonal
3. Not possible

Q. Match the following elements according to the measurements required for the construction of quadrilaterals.

1. 2 diagonals
2. 1 diagonal
3. Not possible

Q. From the options given below, choose the option which has all the measurements you'll require to construct a quadrilateral ABCD.

1. AB, BC, CD and DA

2. AB, BC, CD, AC and BD

3. AB, BC, CD, AC

4. AB & BC

Q.

Construct a quadrilateral $PQRS,$ where $PQ=3.5cm,QR=6.5cm,\angle P=\angle R={105}^{\circ }$ and $\angle S={75}^{\circ }.$

Q. Construct a quadrilateral $ABCD$ in which $BC=4cm,CA=5.6cm,AD=4.5cm,CD=5cm$ and $BD=6.5cm$.

Q.

While constructing quadrilateral PQRS with 3 sides and 2 diagonals which of the following geometric tool is not used?

1. Protractor

2. Ruler

3. Compass

4. Divider

Q. Match the following elements according to the measurements required for the construction of quadrilaterals.

1. 2 diagonals
2. 1 diagonal
3. Not possible

Q. The construction of the following quadrilateral is possible when _______ is / are given.

1. 4 sides and 1 diagonal
2. 2 sides and 1 angle
3. 5 sides of the quadrilateral
4. 3 sides and 2 diagonals

Q.

Construct, if possible, a quadrilateral ABCD given AB = 6 cm, BC = 3.7 cm, CD = 5.7 cm, AD = 5.5 cm and BD = 6.1 cm. Give reasons for not being able to construct it, if you cannot.

Q. The construction of the following quadrilateral is possible when _______ is / are given.

1. 4 sides and 1 diagonal
2. 3 sides and 2 diagonals
3. 5 sides of the quadrilateral
4. 2 sides and 1 angle

Q. To construct a unique quadrilateral ABCD, the measurements of should be given.

1. AB, BD
2. AB, BC, BD
3. AC, BD, AB, BC, CD
4. AC, BD, AB, BC

Q. If the measure of 3 sides of a quadrilateral is given, which among the following measurements are required to construct a unique quadrilateral?

1. 1 angle
2. 2 diagonals
3. 1 diagonal
4. 1 side

Q.

When we start constructing a quadrilateral whose 2 diagonals and 3 sides known, in how many ways can the construction be started.

1. 1

2. 2

3. 3

4. 4