Question 2 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$

Question 3 :
The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

Question 4 :
In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>

Question 5 :
Which of the following numbers form pythagorean triplet?&#160;<br/>i) $2, 3, 4$<br/>ii) $6, 8, 10$<br/>iii) $9, 10, 11$<br/>iv) $8, 15, 17$

Question 6 :
Which of the following could be the side lengths of a right triangle?

Question 7 :
Triangle ABC is right -angled at C. Find&#160;BC,&#160;If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal.&#160;

Question 8 :
The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:

Question 9 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$

Question 10 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $

Question 11 :
The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$

Question 12 :
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 13 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find&#160;$a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 14 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 15 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 16 :
What is the ratio of the areas of two similar triangles whose corresponding sides are in the ratio 15:19?

Question 17 :
If $\triangle ABC$ is similar to $\triangle DEF$ such that BC=3 cm, EF=4 cm and area of $\triangle ABC=54 {cm}^{2}$. Determine the area of $\triangle DEF$.

Question 18 :
If $A={30}^{\circ},\,a=100,\,c=100\sqrt{2}$, find the number of triangles that can be formed.

Question 19 :
Two $\triangle sABC $ and DEF are similar. If $ar(DEF)= 243\ cm^2, ar(ABC)=108\ cm^2$ and $BC= 6\ cm$. Find $EF$.

Question 20 :
State true or false:<br/>Triangle $ABC$ is similar to triangle $PQR$. If $AD$ and $PM$ are altitudes of the two triangles, then<br/>$\displaystyle \dfrac{AB}{PQ}=\dfrac{AD}{PM}.$<br/>

Question 21 :
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 22 :
The perimeter of two similar triangle are $30\ cm$ and $20\ cm$. If one side of first triangle is $12\ cm$ determine the corresponding side of second triangle.

Question 24 :
If $\Delta ABC \sim \Delta PQR$ and $\displaystyle {{PQ} \over {AB}} = {5 \over 2}$ then area $(\Delta ABC):$ area $(\Delta PQR) = ?$

Question 25 :
Two angles of triangle ABC are $\displaystyle 85^{\circ}$ and $\displaystyle 65^{\circ}$ whilethe two angles of another triangle DEF are $\displaystyle 30^{\circ}$ and $\displaystyle 65^{\circ}$.Which of the statements is correct?<br>

Question 26 :
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 27 :
The areas of two similar triangles are $49 \ {cm}^{2}$ and $64 \ {cm}^{2}$ respectively. The ratio of their corresponding sides is:

Question 28 :
If in$\displaystyle \triangle ABC$ and$\displaystyle\triangle DEF$,$\displaystyle \frac{AB}{DE}=\frac{BC}{FD}$ then they will be similar if

Question 29 :
$\Delta ABC&#160;\sim &#160;\Delta PQR$ and $\displaystyle\frac{A(&#160;\Delta ABC)}{A(&#160;\Delta PQR)}=\dfrac{16}{9}$. If $PQ=18$ cm&#160;and $BC=12$ cm, then $AB$ and $QR$ are respectively:

Question 30 :
Find a relationship between $x$ and $y$ so that the triangle whose vertices are given by $(x,y),(1,1)$ and $(5,1)$ is a right triangle with the hypotenuse defined by the points $(1,1)$ and $(5,1)$.

Question 31 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 32 :
Let&#160;$\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let&#160;$\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let&#160;$\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let&#160;$\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?

Question 33 :
Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>