Question 1 :
The perimeter of rectangle is $140$ cm. If the sides are in the ratio $3 : 4$, find the lengths of the four sides and the two diagonals
Question 2 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $16:25$. Find the ratio of their corresponding heights.
Question 3 :
State true or false:<br/>In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD intersect each other at point P, then<br/>$\displaystyle \Delta APB$ is similar to $\displaystyle \Delta CPD.$<br/><br/>
Question 4 :
Assertion: $\triangle ABC$ and $\triangle DEF$ are two similar triangles such that $BC= 4$ cm, $EF = 5$ cm and $A(\triangle ABC) = 64 \:cm^2$, then $A(\triangle DEF) = 100\:cm^2$.
Reason: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Question 5 :
State true or false:<br/>Triangle $ABC$ is similar to triangle $PQR$. If $AD$ and $PM$ are corresponding medians of the two triangles. Then,<br/>$\displaystyle \dfrac{AD}{PQ}=\dfrac{AD}{PM}.$<br/>
Question 6 :
The sides of a triangle are in the ratio 4 : 6 : 7. Then<br>
Question 7 :
Instead of walking along two adjacent sides of a rectangular field,a boy book a short - cut along the diagonal of the field and saved a distance equal to 1/2 the longer side. The ratio of the shorter side of the rectangle to the longer side was:.
Question 8 :
Choose and write the correct alternative.<br>Out of the following which is aPythagorean triplet ?<br>
Question 9 :
$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid point of $BC$. Ratio of the areas of triangle $ABC$ and $BDE$ is
Question 10 :
STATEMENT - 1 : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.<br>STATEMENT - 2 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.<br>
Question 11 :
The Pythagoras theorem , In the right triangle, the square of thehypotenuse is equal to the sum of other two sides. What are we proving here?
Question 12 :
If in $\triangle $s $ABC$ and $DEF,$ $\angle A=\angle E=37^{\circ}, AB:ED=AC:EF$ and $\angle F=69^{\circ},$ then what is the value of $\angle B\: ?$<br>
Question 13 :
If $\triangle ABC\sim \triangle QRP,\dfrac{Ar(ABC)}{Ar(QRP)}=\dfrac{9}{4}$,$AB=18\ cm$ and $BC=15\ cm$; then $PR$ is equal to:<br/>
Question 14 :
The areas of two similar triangles are $81\ cm^{2}$ and $49\ cm^{2}$. If the altitude of the bigger triangle is $4.5\ cm$, find the corresponding altitude of the smaller triangle.
Question 15 :
In a triangle, sum of squares of two sides is equal to the square of the third side.
Question 16 :
$\Delta ABC \sim \Delta PQR$ and areas of two similar triangles are $64$sq.cm and $121$sq.cm respectively. If $QR=15$cm, then find the value of side BC.
Question 17 :
<b></b>The areas of two similar triangles are 100 $cm^2$ and 64 $cm^2$. If the median of greater side of first triangle is 13 cm, find the corresponding median of the other triangle.
Question 18 :
Given $\Delta ABC-\Delta PQR$. If $\dfrac{AB}{PQ}=\dfrac{1}{3}$, then find $\dfrac{ar\Delta ABC}{ar\Delta PQR'}$.
Question 19 :
The areas of two similar triangles are $121$ cm$^{2}$ and $64$ cm$^{2}$, respectively. If the median of the first triangle is $12.1$ cm, then the corresponding median of the other is:<br/>
Question 20 :
If two triangles are similar then, ratio of corresponding sides are:
Question 21 :
$\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF$ are two similar triangles such that $\displaystyle \angle A={ 45 }^{ \circ  },\angle E={ 56 }^{ \circ  }$, then $\displaystyle \angle C$ =___.<br/>
Question 22 :
The perimeter of two similar triangles $\triangle ABC$ and $\triangle DEF$ are $36$ cm and $24$ cm respectively. If $DE=10 $ cm, then $AB$ is :
Question 23 :
In $\Delta ABC$, $D$ is a point on $BC$ such that $3BD = BC$. If each side of the triangle is $12 cm$, then $AD$ equals:
Question 24 :
If corresponding sides of two similar triangles are in the ratio of $4 : 9$, then areas of these triangles are in the ratio of:
Question 25 :
The corresponding sides of two similar triangles are in the ratio $a : b$. What is the ratio of their areas?
Question 26 :
In a $\triangle ABC$, $D$ and $E$ are the midpoints of $AB$ and $AC. DE$ is parallel to $BC$. If the area of $\Delta ABC = 60$ sq cm., then the area of the $\Delta ADE$ is equal to:<br/>
Question 27 :
D and E are the points on the sides AB and AC respectively of triangle ABC such that $ DE||BC$. If area of $ \triangle DBC =15 cm^2$, then area of $\triangle EBC $ is:<br/>
Question 28 :
In Pythagoras theorem triplets the lengths of the sides of the right angled triangle are in the ratio.
Question 29 :
In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If $AO=2CO$ and $BO=2DO$; Then,$\displaystyle \Delta AOB$ is similar to $\displaystyle \Delta COD$<br/>
Question 30 :
State true or false:<br/>In parallelogram $ ABCD $. $ E $ is the mid-point of $ AB $ and $ AP $ is parallel to $ EC $<b> </b>which meets $ DC $ at point $ O $ and $ BC $ produced at $ P $. Hence $ O $ is mid-point of $ AP $.<br/><br/>
