Question 1 :
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

Question 2 :
It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.

Question 3 :
The sides of a triangle are in the ratio 4 : 6 : 7. Then<br>

Question 4 :
The lengths of the sides of a right triangle are $5x + 2$, $5x$ and $3x - 1$.&#160;If $x &gt; 0$ then the length of each side is?

Question 5 :
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 6 :
If $\triangle ABC\sim \triangle &#160;PQR,$ &#160;$ \cfrac{ar(ABC)}{ar(PQR)}=\cfrac{9}{4}$, &#160;$AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:

Question 7 :
Aline segment DE is drawn parallel to base BC of $\Delta\,ABC$ which cuts ABat point D and AC at point E. If AB = 5 BD and EC = 3.2 cm. Find the length ofAE.

Question 8 :
<p>Which among the following is/are correct?<br/>(I) If the altitudes of two similar triangles are in the ratio $2:1$, then the ratio of their areas is $4 : 1$.<br/>(II)&#160;$PQ \parallel BC$ and $AP : PB=1:2$. Then, $\dfrac{A(\triangle APQ)}{A(\triangle ABC)}=\dfrac{1}{4}$</p>

Question 9 :
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 10 :
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 11 :
Through a point $P$ inside the triangle $ABC$ a line is drawn parallel to the base $AB$, dividing the triangle into two equal area. If the altitude to $AB$ has a length of $1$, then the distance from $P$ to $AB$ is

Question 12 :
Three sides of a triangle are 6 cm, 12 cm and 13 cm then<br>

Question 13 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 14 :
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>