Question 1 :
The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............
Question 2 :
Triangle A has a base of x and a height of 2x. Triangle B is similar to triangle A, and has a base of 2x. What is the ratio of the area of triangle A to triangle B?
Question 3 :
State true or false:<br/>The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.
Question 4 :
State true or false:<br/>The ratio of the areas of two triangles on the same base is equal to the ratio of their heights.
Question 6 :
 If the two legs of a right angled $\Delta$ are equal and the square of the hypotenuse is $100,$ then the length of each leg is:
Question 7 :
In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
Question 8 :
If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by
Question 9 :
Which of the following can be the sides of a right angled triangle ?
Question 10 :
In $\triangle{ABC}$, $\angle{B}=90$, $AB=8\:cm$ and $BC=6\:cm$.The length of the median BM is
Question 11 :
In $\Delta$ ABC, $\angle B = 90$, AB = 8 cm and BC = 6 cm. The length of the median BM is<br>
Question 12 :
We use ........... formula to find the lengths of the right angled triangles.
Question 13 :
In the $\triangle LMN$ <b></b>$\displaystyle $, angle L is $\displaystyle { 65 }^{ o }$ $\displaystyle $, angle M is a right angle, what would be angle N?
Question 14 :
A............can never be made up of all odd numbers or two even numbers and one odd number.
Question 15 :
Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$
Question 16 :
A right angled triangle has $24,7cm $ as its sides . What will be its hypotenuse?
Question 17 :
Can we construct sets of Pythagorean Triples with all even numbers?
Question 18 :
 A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.
Question 19 :
It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.
Question 20 :
Is it true that a Pythagorean Triple can never be made up of all oddnumbers?
Question 21 :
If the measures of sides of a triangle are $(x^2-1) cm, (x^2 +1) cm$, and $2x cm$, then the triangle will be: 
Question 22 :
In a $\Delta$ABC, if $AB^2\, =\, BC^2\, +\, AC^2$, then the right angle is at:
Question 23 :
The length of the hypotenuse of a right angled $\Delta$ le whose two legs measure 12 cm and 0.35 m is:
Question 25 :
Select the correct alternative and write the alphabet of that following :<br>Out of the following which is the Pythagorean triplet ?
Question 26 :
If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.
Question 27 :
A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.
Question 28 :
If the lengths of the sides of a triangle does not satisfy the rule of $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$, then that triangle does not contain a
Question 29 :
If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm less than the hypotenuse, the other side b is equal to.
Question 30 :
Which of the following cannot be the sides a right angle triangle?<br>
Question 31 :
Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5
Question 32 :
In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>
Question 33 : <p> In a right angle triangle, the hypotenuse is the greatest side. <br/></p><b>State whether the above statement is true or false.</b><br/>
Question 34 :
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
Question 35 :
A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.
Question 37 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$
Question 38 :
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 39 :
In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>
Question 40 :
Which of the following numbers form pythagorean triplet? <br/>i) $2, 3, 4$<br/>ii) $6, 8, 10$<br/>iii) $9, 10, 11$<br/>iv) $8, 15, 17$
Question 41 :
Which of the following could be the side lengths of a right triangle?
Question 42 :
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 43 :
The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:
Question 44 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$
Question 45 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $
Question 46 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 47 :
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 48 :
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 49 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 50 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 51 :
The ratio of areas of two similar triangles is $81 : 49$. If the median of the smaller triangle is $4.9\ cm$, what is the median of the other?
Question 52 :
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 53 :
If $\triangle ABC$ and $\triangle PQR$ are similar and $\dfrac {BC}{QR} = \dfrac {1}{3}$ find $\dfrac {area (PQR)}{area (BCA)}$
Question 54 :
If two triangles are similar then, ratio of corresponding sides are:
Question 55 :
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 56 :
The lengths of the sides of a right triangle are $5x + 2$, $5x$ and $3x - 1$. If $x > 0$ then the length of each side is?
Question 57 :
Area of similar triangles are in the ratio $25:36$ then ratio of their similar sides is _________?
Question 58 :
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 59 :
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 60 :
In triangle ABC, AD is perpendicular to BC and $AD^{2}\, =\, BD\, \times\, DC.$ Find $\angle BAC$
Question 61 :
$ABC$ 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 62 :
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 63 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $9:16$. Find the ratio of their corresponding heights.
Question 64 :
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 65 :
If a triangle with side lengths as $5, 12$, and $15$ cm is similar to a triangle which has longer side length as $24$ cm, then the perimeter of the other triangle is:
Question 66 :
A right triangle has hypotenuse of length p cm and one side of length q cm. If p-q = 1, express length of the third side of the right triangle in term of p is
Question 67 :
The sides of a triangle are in the ratio 4 : 6 : 7. Then<br>
Question 68 :
Two triangles are similar and their corresponding sides are in the ratio $3 : 5$. Find the ratio of the areas of these triangles.
Question 69 :
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 70 :
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 71 :
If the sides of two similar triangles are in the ratio $1:7$, find the ratio of their areas.<br/>
Question 72 :
ABC is right angled triangle, right angle at B, $AC=25$, $AB=7$ then BC= ? <br/>
Question 73 :
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 74 :
The sides of a triangle are $3x+4y,\,4x+3y$ and $5x+5y$ units, where $x,y>0$.The triangle is ______________.
Question 75 :
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 76 :
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 77 :
Let $\triangle ABC\sim \triangle DEF$ and their areas be, respectively $64\ {cm}^{2}$ and $121\ {cm}^{2}$. If $EF=15.4\ cm$, find $BC$.
Question 78 :
Two triangles ABC and PQR  are similar, if $BC : CA : AB = $1: 2 : 3, then $\dfrac{QR}{PR}$ is<br/>
Question 79 :
$\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$
Question 80 :
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 81 :
The corresponding sides of two similar triangles are in the ratio $a : b$. What is the ratio of their areas?
Question 82 :
A ladder of $3.9m$ length is laid against a wall. The distance between the foot of the wall and the ladder is $1.5m$. Find the height at which the ladder touches the wall.
Question 83 :
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 84 :
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 85 :
For two triangles, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This is called ___ similarity.   
Question 86 :
$\Delta ABC \sim \Delta PQR$ 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 87 :
If the sides of two similar triangles are in the ratio $2 : 3$, then their areas are in the ratio:
Question 88 :
$\triangle ABD \sim \triangle DEF$ 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 90 :
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 91 :
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 92 :
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 93 :
If in$\displaystyle \triangle ABC$ and$\displaystyle\triangle DEF$,$\displaystyle \frac{AB}{DE}=\frac{BC}{FD}$ then they will be similar if
Question 94 :
If $A={30}^{\circ},\,a=100,\,c=100\sqrt{2}$, find the number of triangles that can be formed.
Question 95 :
In a right angled triangle $ABC,\,\angle B=90^{\circ}$ such that $AC=13\;cm,\;BC=5\;cm$. Then, find $AB$.
Question 96 :
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 97 :
The angles of the $\Delta ABC$ and $\Delta DEF$ are given as follows;$A = 90\displaystyle ^{\circ},\ \ B = 30\displaystyle ^{\circ}, \ \ D = 90\displaystyle ^{\circ},$ and $E = 30\displaystyle ^{\circ}$If the side $BC$ is twice the side $EF$, which of the following statement is true?
Question 98 :
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 99 :
$\displaystyle \Delta ABC$ 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 100 :
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 101 :
Let $\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let $\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let $\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let $\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?
Question 102 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by
Question 103 : Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion </td></tr><tr><td>2. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion </td></tr><tr><td>3. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion </td></tr><tr><td>4. In $\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>
