Practical Geometry

Q.

If $A,B$ and $C$ are three sets, then what is $A-(B-C)$ equal to?

1. $A-(B\cap C)$

2. $(A-B)\cup C$

3. $(A-B)\cup (A\cap C)$

4. $(A-B)\cup (A-C)$

Q. Which of the following option(s) can be used to construct a triangle?

1. 3 angles
2. 2 sides and 1 included angle
3. 3 sides
4. 2 angles and an included side

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

4. AB, BC, CD, AC

Q. Construction of similar polygons is similar to that of construction of similar triangles. If you are asked to construct a parallelogram similar to a given parallelogram with a given scale factor, which of the given steps will help you construct a similar parallelogram?

1. Find a point on the larger side which divides it in the ratio of the given scale factor and using the smaller side as the other parallel side to construct the parallelogram.
2. Find two points one on the larger side and other on the smaller side using the given scale factor and use these scaled lengths to construct a similar parallelogram.
3. With one of the vertices as centre and radius - (scale factor multiplied with the length of the larger side). Draw two arcs on the larger and smaller sides. Use these 2 points to construct the parallelogram.
4. None of these helps in constructing a similar parallelogram.

Q. Construct a trapezium ABCD, in which $AD\parallel BC$, AD = 3 cm, AB = 2.5 cm, BC = 5 cm, and CD = 2.8 cm.

Q. Construct a trapezium ABCD, in which $AD\parallel BC$ and AD = 3.0 cm, AB = 2.5 cm, BC = 5.0 cm and CD = 2.8 cm. [4 MARKS]

Q.

How many measurements are sufficient to make a quadrilateral?

1. 3

2. 5

3. 4
4. 6

Q.

A polygon is regular if

1. all of the above

2. all its interior angles are equal

3. all its sides are equal

4. all its exterior angles are equal

Q.

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

1. AB, BC, CD, DA and BD

2. AB, BC, CD, AC and BD

3. AB, BC, CD and DA

4. both options B & C

Q.

The quadrilateral ABCD has given below. Choose the criteria required to construct a quadrilateral from the following options.

1. AB, BC, CD, AC, BD

2. AB, BC, CD, DA, BD

3. Both B & C

4. AB, BC, CD, DA

Q. Sort the steps to construct a parallelogram of sides of length 4 cm, 9 cm and the angle ${60}^{\circ }$.

1. $\mathrm{Draw}\mathrm{angle}{60}^o\mathrm{at}B\mathrm{and}\mathrm{mark}a\mathrm{point}C\mathrm{along}\mathrm{the}\mathrm{same}\mathrm{angle}\mathrm{at}9\mathrm{cm}.$
2. $\mathrm{Join}A,B,C\&D\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{parallelogram}\mathrm{ABCD}.$
3. $\mathrm{Draw}a\mathrm{line}\mathrm{parallel}\mathrm{to}\mathrm{AB}\mathrm{passing}\mathrm{through}C\mathrm{and}\mathrm{measuring}4\mathrm{cm}.\mathrm{Mark}D\mathrm{on}\mathrm{it}.$
4. Draw AB = 4 cm.

Q. In which of the following cases will you not be able to construct a convex quadrilateral?

1. When the length of four sides and one angle are given
2. When the length of two sides and two included angles are given
3. When the length of three sides and the two diagonals are given
4. When the length of three sides and one diagonal are given

Q. Construct a square each of whose sides measures 3.2 cm.

Q. The number of triangles that we can see after the construction of a quadrilateral when 2 adjacent sides and 3 angles are given will be .

1. \N
2. 1
3. 2
4. 3

Q.

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

1. One angle of the parallelogram

2. Two angles of the parallelogram

3. The angle between the diagonals

4. None of the above

Q.

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

1. The angle between the diagonals

2. One angle of the parallelogram

3. Two angles of the parallelogram

4. None of the above

Q. Construct any $△$ABC. Find a point on side BC which is equidistant from sides AB and AC. Justify your construction.

Q. The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.

1. 16 units
2. 24 units
3. 36 units
4. 18 units

Q.

It is possible to draw a unique parallelogram with side lengths 4 cm and 9 cm.

1. True

2. False

Q.

It is possible to draw a unique parallelogram with side lengths 4 cm and 9 cm.

1. False

2. True

Q. A parallelogram is constructed and named KLMN. LP is perpendicular to KL and ML is the angular bisector of $\angle KLP$. Find the value of $\angle KNM$.

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q.

A polygon having eight sides, is called:

1. Octagon

2. Pentagon

3. Hexagon

4. Heptagon

Q.

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

1. AB, BC, CD, AC and BD

2. both options B & C

3. AB, BC, CD, DA and BD

4. AB, BC, CD and DA

Q.

What are the minimum number of measurements required to construct a unique parallelogram?

1. 3

2. 2
3. 1
4. 5

Q. Sort the steps to construct a parallelogram of sides of length 4 cm, 9 cm and the angle ${60}^{\circ }$.

1. $\mathrm{Join}A,B,C\&D\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{parallelogram}\mathrm{ABCD}.$
2. Draw AB = 4 cm.
3. $\mathrm{Draw}\mathrm{angle}{60}^o\mathrm{at}B\mathrm{and}\mathrm{mark}a\mathrm{point}C\mathrm{along}\mathrm{the}\mathrm{same}\mathrm{angle}\mathrm{at}9\mathrm{cm}.$
4. $\mathrm{Draw}a\mathrm{line}\mathrm{parallel}\mathrm{to}\mathrm{AB}\mathrm{passing}\mathrm{through}C\mathrm{and}\mathrm{measuring}4\mathrm{cm}.\mathrm{Mark}D\mathrm{on}\mathrm{it}.$

Q.

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

1. None of the above

2. The angle between the diagonals

3. One angle of the parallelogram

4. Two angles of the parallelogram

Q. In what ratio does the centroid of the triangle divide each median of the triangle?

1. 2 : 1
2. 3 : 1
3. 4 : 1
4. 5 : 1

Q. The minimum number of measurements required to construct a quadrilateral is ___. Choose the most appropriate answer to fill in the blank.

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

Q.

There is a quadrilateral with 2 sides and 2 diagonals given. How many more pieces of data need to be provided to construct the quadrilateral ?

___