Question 13 Marks
Construct a parallelogram PQRS in which $QR =4.7 cm, \angle Q =120$ and $PQ =2.8 cm$.
Answer
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Questions
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28 questions · timed · auto-graded
Question 23 Marks
Construct a parallelogram ABCD in which $BC =6 cm, CD =4 cm$ and $\angle C =60$.
Answer
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Question 33 Marks
Construct a parallelogram ABCD in which AB = 4.8cm BC = 3.5 cm and diagonal AC = 5.4 cm.
Answer
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Question 43 Marks
Construct a parallelogram ABCD in which BC = 5 cm CD = 3 cm and diagonal BD = 6 cm.
Answer
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Question 53 Marks
In the given figure, ABCD is a kite whose diagonals intersect at O . If $\angle DAB =54$ and $\angle BCD =76$, calculate :
(i) $\angle ODA$
(ii) $\angle OBC$.
(i) $\angle ODA$
(ii) $\angle OBC$.
Answer
View full question & answer→$\angle ODA =63, \angle OBC =52$
Question 63 Marks
In the given figure, ABCD is a rectangle whose diagonals intersect at O. Diagonal AC is produced to E and $\angle ECD =140$. Find the angles of $\triangle OAB$.
Answer
View full question & answer→$\angle OAB =40, \angle ABO =40, \angle AOB =100$
Question 73 Marks
In the adjoining figure, ABCD is a rhombus whose diagonals intersect at O .
If $\angle OAB : \angle OBA =2: 3$, find the angles of $\triangle OAB$.
If $\angle OAB : \angle OBA =2: 3$, find the angles of $\triangle OAB$.
Answer
View full question & answer→$\angle AOB =90, \angle OAB =36, \angle OBA =54$
Question 83 Marks
In the given figure, ABCD is a parallelogram and E is the mid-point of BC. If DE and AB produced meet at F, prove that AF = 2AB.
Answer
View full question & answer→[Hint. $\triangle D E C \cong \triangle F E B$.
Question 93 Marks
In the adjoining figure, ABCD is a parallelogram and $X$ is the mid-point of $B C$. The line $A X$ produced meets DC produced at Q. The parallelogram AQPB is completed.
Prove that :
(i) $\triangle ABX \cong \triangle QCX$.
(ii) $DC = CQ = QP$.
Prove that :
(i) $\triangle ABX \cong \triangle QCX$.
(ii) $DC = CQ = QP$.
Answer
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Question 103 Marks
In the adjoining figure, ABCD and PQBA are two parallelograms. Prove that :
(i) DPQC is a parallelogram.
(ii) $DP = CQ$
(iii) $\triangle DAP \cong \triangle CBQ$.
(i) DPQC is a parallelogram.
(ii) $DP = CQ$
(iii) $\triangle DAP \cong \triangle CBQ$.
Answer
View full question & answer→[Hint. $D C \| A B$ and $A B\|P Q \Rightarrow D C\| P Q$. $D C=A B$ and $A B=P Q \Rightarrow D C=P Q$.]
Question 113 Marks
In the given figure, ABCD is a parallelogram in which $\angle A =70$. Calculate $\angle B , \angle C$ and $\angle D$.
Answer
View full question & answer→$\angle B =110, \angle C =70, \angle D =110$
Question 123 Marks
You have been given following specification regarding a quadrilateral. Measure of all the four angles and the length of one side is given. Would you be able to construct a unique quadrilateral in this case? Justify your answer.
Answer
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Question 133 Marks
ABCD is a rectangle in which diagonal BD bisects$\angle B$. Can we definitely say that ABCD is a square?
Answer
View full question & answer→yes
Question 143 Marks
Construct a parallelogram ABCD in which $AB =4.8 cm, BC =3.5 cm$ and diagonal $AC =5.4 cm$.
Answer
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Question 153 Marks
Construct a parallelogram ABCD in which $BC =5 cm, CD =3 cm$ and diagonal $BD =6 cm$.
Answer
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Question 163 Marks
Construct a parallelogram PQRS in which $QR =4.7 cm, \angle Q =120^{\circ}$ and $PQ =2.8 cm$.
Answer
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Question 173 Marks
Construct a parallelogram ABCD in which $BC =6 cm, CD =4 cm$ and $\angle C =60^{\circ}$.
Answer
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Question 183 Marks
Construct a quadrilateral ABCD in which $AB = AD =5.3 cm, BC = CD =5 cm$ and diagonal $BD =6.4 cm$.
Answer
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Question 193 Marks
In the given figure, $A B C D$ is a parallelogram and $E$ is the mid-point of $B C$. If $D E$ and $A B$ produced meet at $F$, prove that $A F=2 A B$.
Answer
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Question 203 Marks
Show that the bisectors of the angles of a parallelogram enclose a rectangle.
Answer
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Question 213 Marks
In the given figure, ABCD is a parallelogram and $X , Y$ are points on diagonal $B D$ such that $D X=B Y$. Prove that CXAY is a parallelogram.
Answer
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Question 223 Marks
In the adjoining figure, ABCD and PQBA are two parallelograms. Prove that:
(i) DPQC is a parallelogram.
(ii) $DP = CQ$.
(iii) $\triangle DAP \cong \triangle CBQ$.
(i) DPQC is a parallelogram.
(ii) $DP = CQ$.
(iii) $\triangle DAP \cong \triangle CBQ$.
Answer
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Question 233 Marks
If one angle of a parallelogram is $90^{\circ}$, show that each of its angles measures $90^{\circ}$.
Answer
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Question 243 Marks
DEC is an equilateral triangle in a square ABCD . If BD and CE intersect at O and $\angle COD =x^{\circ}$, find the value of $x$.
Answer
View full question & answer→$75^{\circ}$
Question 253 Marks
In the given figure, $A B C D$ is a rectangle whose diagonals intersect at O . Diagonal AC is produced to E and $\angle ECD =140^{\circ}$. Find the angles of $\triangle OAB$.
Answer
View full question & answer→$\angle OAB =40^{\circ}, \angle ABO =40^{\circ}, \angle AOB =100^{\circ}$
Question 263 Marks
In the adjoining figure, ABCD is a rhombus whose diagonals intersect at O .
If $\angle OAB : \angle OBA =2: 3$, find the angles of $\triangle OAB$.
If $\angle OAB : \angle OBA =2: 3$, find the angles of $\triangle OAB$.
Answer
View full question & answer→$\angle AOB =90^{\circ}, \angle OAB =36^{\circ}, \angle OBA =54^{\circ}$
Question 273 Marks
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Answer
View full question & answer→$108^{\circ}, 72^{\circ}, 108^{\circ}, 72^{\circ}$
Question 283 Marks
In the given figure, ABCD is a parallelogram in which $\angle A =70^{\circ}$. Calculate $\angle B , \angle C$ and $\angle D$.
Answer
View full question & answer→$\angle B =110^{\circ}, \angle C =70^{\circ}, \angle D =110^{\circ}$