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MATHEMATICS [4 marks sum]

Quadrilaterals · ICSE STD 9 (ICSE - English Medium). 15 questions.

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[4 marks sum]

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15 questions · timed · auto-graded

Question 14 Marks
In the given figure, ABCD is a parallelogram. Side DC is produced to E and $\angle BCE =105$.
Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
Image
Answer
$\angle A =75, \angle B=105, \angle C =75, \angle D =105$
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Question 24 Marks
DEC is an equilateral triangle in a square ABCD . If BD and CE intersect at O and $\angle COD =x$, find the value of $x$.
Image
Answer
75
[Hint. $\angle C D O=45$ and $\angle C D E=60 \Rightarrow \angle O D E=15$.
$\angle D O C=\angle O D E+\angle D E C=(15+60)=75$.
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Question 34 Marks
Which of the following quadrilaterals can you construct if you know the length of two its diagonals?
Parallelogram$\quad$Rectangle$\quad$Rhombus$\quad$Square
Answer
Rhombus and Square
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Question 44 Marks
In the given figure, ABCD is a rhombus in which $\angle A =72^{\circ}$. If $\angle CBD =x^{\circ}$, find the value of $x$.
Image
Answer
$x=54$
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Question 54 Marks
In the adjoining figure, equilateral $\triangle E D C$ surmounts square ABCD . If $\angle DEB =x^{\circ}$, find the value of $x$.
Image
Answer
$x=45$
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Question 74 Marks
Construct a parallelogram ABCD in which diagonal $AC =5.6 cm$, diagonal $BD =6.2 cm$ and angle between them is $60^{\circ}$.
Answer
self
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Question 84 Marks
Construct a quadrilateral XYZT in which $XY = XZ =5.7 cm, YZ =4.5 cm, ZX =4.6 cm$ and $XT =5 cm$.
Answer
self
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Question 94 Marks
Construct a quadrilateral ABCD in which $AB = CD =5.1 cm, BC =4.7 cm$, $DA =4.2 cm$ and $\angle BCD =60^{\circ}$.
Answer
self
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Question 104 Marks
If a diagonal of a parallelogram bisects one of the angles of the parallelogram, prove that it also bisects the second angle and then the two diagonals are perpendicular to each other.
Answer
self
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Question 114 Marks
In the adjoining figure, ABCD is a parallelogram. Line segments $A X$ and $C Y$ bisect $\angle A$ and $\angle C$ respectively.
Prove that:
(i) $\triangle ADX \cong \triangle CBY$
(ii) $AX = CY$
(iii) $A X \| C Y$
(iv) AYCX is a parallelogram.
Image
Answer
self
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Question 124 Marks
In the given figure, ABCD is a trapezium in which
$
\angle A=(x+25)^{\circ}, \angle B=y^{\circ}, \angle C=95^{\circ} \text { and } \angle D=(2 x+5)^{\circ}
$
Find the values of $x$ and $y$.
Image
Answer
$x=50, y=85$
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Question 134 Marks
In the given figure, $A B C D$ is an isosceles trapezium in which $\angle CDA =2 x^{\circ}$ and $\angle BAD =3 x^{\circ}$.
Find all the angles of the trapezium.
Image
Answer
$\angle A =108^{\circ}, \angle C =72^{\circ}, \angle D =72^{\circ}, \angle B =108^{\circ}$
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Question 144 Marks
In the given figure, ABCD is a kite whose diagonals intersect at O . If $\angle DAB =54^{\circ}$ and $\angle BCD =76^{\circ}$, calculate :
(i) $\angle ODA$
(ii) $\angle OBC$.
Image
Answer
$\angle ODA =63^{\circ}, \angle OBC =52^{\circ}$
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Question 154 Marks
In the given figure, $A B C D$ is a parallelogram. Side $D C$ is produced to E and $\angle BCE =105^{\circ}$.
Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
Image
Answer
$\angle A =75^{\circ}, \angle B =105^{\circ}, \angle C =75^{\circ}, \angle D =105^{\circ}$
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[4 marks sum] - MATHEMATICS STD 9 Questions - Vidyadip