Question 1 :
Which of the following could be the side lengths of a right triangle?
Question 2 :
Triangle ABC is right -angled at C. Find BC, If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal. 
Question 3 :
The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:
Question 4 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$
Question 5 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $
Question 6 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 7 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 8 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 9 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 10 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 11 :
Triangles ABC and DEF are similar. If their areas are 64 $cm^2$ and 49 $cm^2$ and if AB is 7 cm, then find the value of DE.
Question 12 :
What is the ratio of the areas of two similar triangles whose corresponding sides are in the ratio 15:19?
Question 13 :
ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed in sides AC and AB. Find the ratio between the areas of $\triangle ABE$ and $\triangle ACD$.
Question 14 :
If the sides of two similar triangles are in the ratio $1:7$, find the ratio of their areas.<br/>
Question 15 :
$\Delta ABC \sim  \Delta PQR$ and $\displaystyle\frac{A( \Delta ABC)}{A( \Delta PQR)}=\dfrac{16}{9}$. If $PQ=18$ cm and $BC=12$ cm, then $AB$ and $QR$ are respectively:
Question 16 :
The perimeters of two similar triangles are $24$ cm. and $18$ cm. respectively. If one side of first triangle is $8$ cm., what is the corresponding side of the other triangle.<br/>
Question 17 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $9:16$. Find the ratio of their corresponding heights.
Question 18 :
The sides of a right triangle are $(x-1)$, $x$ and $(x+1)$. Find the sides of the triangle.
Question 19 :
$\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$
Question 20 :
If $\triangle ABC\sim \triangle  PQR,$  $ \cfrac{ar(ABC)}{ar(PQR)}=\cfrac{9}{4}$,  $AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:
Question 21 :
In $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2\ cm$ and $DE = 1.4\ cm$. Find the ratio of areas of $\triangle ABC$ and $\triangle DEF$.
Question 22 :
State true or false:<br/>In $\triangle ABC$, $\angle A$ is obtuse and $AB= AC$. $P$ is any point in side $BC$. $\displaystyle PM \perp AB$<br/>and $\displaystyle PN \perp AC.$<br/>Then, $\displaystyle PM \times PC= PN \times PB$<br/>
Question 23 :
In similar triangles $\triangle ABC$ and $\triangle FDE, DE = 4 cm, BC = 8 cm$ and area of $\triangle FDE = 25 cm^2$. What is the area of $\Delta ABC$?
Question 24 :
Two triangles ABC and PQR  are similar, if $BC : CA : AB = $1: 2 : 3, then $\dfrac{QR}{PR}$ is<br/>
Question 25 :
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 26 :
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $\Delta\,BPC$ is similar to $\Delta\,ABC$. Also, find the length of BP.
Question 27 :
$\triangle ABD \sim \triangle DEF$ and the perimeters of $\triangle ABC$ and $\triangle DEF$ are $30 cm$ and $18 cm$ respectively. If $BC = 9 cm$, calculate measure of $EF$.
Question 28 :
$\Delta ABC \sim \Delta PQR$ 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 29 :
In $\Delta ABC \sim  \Delta PQR$, $M$ is the midpoint of $BC$ and $N$ is the midpoint of $QR$. If the area of $\Delta ABC =$ $100$ sq. cm and the area of $\Delta PQR =$ $144$ sq. cm. If $AM = 4$ cm, then $PN$ is:<br/>
Question 30 :
State true or false:<br/>Triangle $ABC$ is similar to triangle $PQR$. If bisector of $\angle BAC$ meets $BC$ at point $D$ and the bisector of $\angle QPR$ meets $QR$ at point $M$, Then, $\displaystyle \dfrac{AB}{PQ}=\dfrac{AC}{PM}.$<br/>
Question 31 :
$\displaystyle \Delta ABC$ 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 32 :
If the sides of a right-angled triangle are $\displaystyle \left \{ \cos 2\alpha +\cos 2\beta +2\cos \left ( \alpha +\beta  \right ) \right \}$ and $\displaystyle \left \{ \sin 2\alpha +\sin 2b+2\sin (\alpha +\beta ) \right \},$ then the length of the hypotenuse is: 
Question 33 :
Two isosceles triangles have their corresponding angles equal and their areas are in the ratio $25 : 36$. Find the ratio of their corresponding heights
Question 34 :
In triangle ABC, AD is perpendicular to BC and $AD^{2}\, =\, BD\, \times\, DC.$ Find $\angle BAC$
Question 35 :
The hypotenuse of a right triangle is $6$ m more than twice the shortest side. If the third side is $2$ m less than the hypotenuse, find the hypotenuse of the triangle.<br>
