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&#160;BC,&#160;If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal.&#160;

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.&#160;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&#160;$a$ 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 :
Three sides of a triangle are 6 cm, 12 cm and 13 cm then<br>

Question 12 :
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 13 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $9:16$. Find the ratio of their corresponding heights.

Question 14 :
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 15 :
The area of two similar triangles are in ratio 16:81. Find the ratio of its sides.

Question 16 :
D and E are respectively the points on the sides AB and AC of a $\displaystyle \Delta ABC$&#160;such that $AB = 12 cm$, $AD = 8 cm$, $AE = 12 cm$ and $AC = 18 cm$, then

Question 17 :
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 18 :
If the sides of two similar triangles are in the ratio $2 : 3$, then their areas are in the ratio:

Question 19 :
Area of similar triangles are in the ratio $25:36$ then ratio of their similar sides is _________?

Question 20 :
In a right triangle, the square of the hypotenuse is $x$ times the sum of the squares of the other two sides. The value of $x$ is:<br/>

Question 21 :
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 23 :
ABC is right angled triangle, right angle at B, $AC=25$, $AB=7$ then BC= ? <br/>

Question 24 :
For $\Delta ABC$ &amp; $\Delta PQR$, if $m \angle A = m \angle R$ and $m \angle C = m \angle Q$, then $ABC \leftrightarrow$ ............. is a similarity.

Question 25 :
The sides of a triangle are $5$ cm, $6$ cm and $7$ cm. One more triangle is formed by joining the midpoints of the sides. The perimeter of the second triangle is:<br/>

Question 26 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 27 :
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 28 :
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>