Construction of Parallelogram Given Its Sides and Area

Q.

A parallelogram can be constructed uniquely if

1. measurement of one side is given

2. the measurement of one angle is given

3. measurement of two diagonals is given

4. the measurement of two adjacent sides and a diagonal is given

Q.

Given the length of 2 adjacent sides, a parallelogram can be constructed if

1. the included angle is given

2. one diagonal is given

3. two diagonals are given

4. All of the these

Q.

Which of the following measurements are necessarily needed to construct a parallelogram uniquely?

1. Two diagonals

2. Two sides

3. One side and one diagonal

4. Two sides and one diagonal

Q.

Given the length of two diagonals of a parallelogram, we need measurement of at least

1. three sides

2. one side

3. two sides

4. four sides

Q. Which of the following properties are used in the construction of a parallelogram given the measure of two sides and the angle between them?

1. Opposite sides are equal.
   
2. Opposite sides are parallel.
3. Corresponding angles are equal.
4. Diagonals bisect each other.

Q. In which of the following cases is the construction of a parallelogram possible?

1. Measure of two adjacent sides.
2. Measure of two consecutive sides and included angle.
3. Measure of two adjacent sides and height are given.
4. Measure of two diagonals.

Q. A parallelogram can be constructed if the length of the diagonals and the angle between them is known.

1. False
2. True

Q. Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.

इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 75°. The angles of the parallelogram are a° and b° such that a < b. Also, rhombus ABCD of side 10 cm has one of its angles as a° – 15°. If O is the point of intersection of angle bisectors of any two adjacent angles of the given parallelogram, then the angle made between these angle bisectors is x. Based on the given information, answer the following question. Match the Columns and choose the appropriate answer.

एक समान्तर चतुर्भुज जिसके अधिककोण वाले शीर्ष से डाले गये दो शीर्षलम्बों के मध्य कोण 75° है। समान्तर चतुर्भुज के कोण a° व b° हैं जबकि a < b है तथा 10 cm भुजा वाले समचतुर्भुज ABCD का एक कोण a° – 15° है। यदि दिए गए समान्तर चतुर्भुज के किन्हीं दो आसन्न कोणों के कोण समद्विभाजकों का प्रतिच्छेदी बिंदु O है, तब इन कोण समद्विभाजकों के मध्य निर्मित कोण x है। दी गयी सूचना के आधार पर निम्नलिखित प्रश्न का उत्तर दीजिए। कॉलमों का मिलान करें और सही उत्तर चुनें।

	Column I कॉलम I		Column II कॉलम II
(A)	The value of b is b का मान है	(P)	Complement of 15° 15° का पूरक कोण
(B)	The length of longer diagonal of rhombus ABCD (in cm) is समचतुर्भुज ABCD के लम्बे विकर्ण की लम्बाई (cm में) है	(Q)	105
(C)	The measure of a° is a° की माप है	(R)	$10\sqrt{3}$
(D)	The measure of x + 15° (in degrees) is x + 15° का माप (डिग्री में) है	(S)	5° more than the supplement of 110° 110° के संपूरक कोण से 5° अधिक

1. A-PS, B-S, C-Q, D-P
2. A-RS, B-Q, C-R, D-R
3. A-Q, B-R, C-PS, D-Q
4. A-S, B-P, C-QR, D-S

Q.

If the diagonal of a parallelogram is known then which of the following is required to construct the parallelogram?

1. Pair of opposite angles

2. Pair of adjacent sides

3. Pair of opposite sides

4. Pair of adjacent angles

Q. Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

Q.

Which of the following measurements are necessarily needed to construct a parallelogram uniquely?

1. Two sides and one diagonal

2. One side and one diagonal

3. Two diagonals

4. Two sides

Q. A parallelogram can be constructed if the length of the diagonals and the angle between them is known.

1. False
2. True

Q.

If the diagonal of a parallelogram is known then which of the following is required to construct the parallelogram?

1. Pair of adjacent sides

2. Pair of opposite angles

3. Pair of opposite sides

4. Pair of adjacent angles

Q. A parallelogram can be constructed if the length of the diagonals and the angle between them is known.

1. False
2. True

Q. Burst the bubbles in which the parameters are sufficient to construct a parallelogram.

1. 2-sides
   1-angle
2. 2-side
   1-diagonal
3. 1-side
   1-diagonal
4. 2-diagonals
5. 2-side
   1-Altitude
6. 2-diagonal
   1angle
7. 1-side
   1-diagonal
8. 2-sides &
   Area

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.
इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 75°. The angles of the parallelogram are a° and b° such that a < b. Also, rhombus ABCD of side 10 cm has one of its angles as a° – 15°. If O is the point of intersection of angle bisectors of any two adjacent angles of the given parallelogram, then the angle made between these angle bisectors is x. Based on the given information, match the Columns and choose the appropriate answer.

एक समान्तर चतुर्भुज जिसके अधिककोण वाले शीर्ष से डाले गए दो शीर्षलम्बों के मध्य कोण 75° है। समान्तर चतुर्भुज के कोण a° व b° हैं जबकि a < b है तथा 10 cm भुजा वाले समचतुर्भुज ABCD का एक कोण a° – 15° है। यदि दिए गए समान्तर चतुर्भुज के किन्हीं दो आसन्न कोणों के कोण समद्विभाजकों का प्रतिच्छेदी बिंदु O है, तब इन कोण समद्विभाजकों के मध्य निर्मित कोण x है। दी गयी सूचना के आधार पर कॉलमों का मिलान करें और सही उत्तर चुनें।

	Column I कॉलम I		Column II कॉलम II
(A)	The value of b is b का मान है	(P)	Complement of 15° 15° का पूरक कोण
(B)	The length of longer diagonal of rhombus ABCD (in cm) is समचतुर्भुज ABCD के लम्बे विकर्ण की लम्बाई (cm में) है	(Q)	105
(C)	The measure of a° is a° की माप है	(R)	$10\sqrt{3}$
(D)	The measure of x + 15° (in degrees) is x + 15° का माप (डिग्री में) है	(S)	5° more than the supplement of 110° 110° के संपूरक कोण से 5° अधिक

1. A-P, B-QR, C-PS, D-Q
2. A-Q, B-QR, C-S, D-QS
3. A-PQ, B-RS, C-S, D-Q
4. A-Q, B-R, C-PS, D-Q