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&#160;the same height is equal to the ratio of&#160;their bases.

Question 4 : State true or false:<br/>The ratio of the areas of two triangles on&#160;the same base is equal to the ratio of&#160;their heights.

Question 6 : &#160;If the two legs of a right angled&#160;$\Delta$ are&#160;equal and the square of the hypotenuse&#160;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 $\triangle LMN$&#160;<b></b>$\displaystyle $, angle L is&#160;$\displaystyle { 65 }^{ o }$&#160;$\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 : &#160;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:&#160;

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&#160;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>&#160;In a right angle triangle, the hypotenuse is the&#160;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.&#160;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?&#160;<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&#160;BC,&#160;If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal.&#160;

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.&#160;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&#160;$a$ 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 : 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. &#160;&#160;

Question 52 : 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 53 : <b></b>The areas of two similar triangles are 100 $cm^2$ and 64 $cm^2$. If the median of greater side of first triangle is 13 cm, find the corresponding median of the other triangle.

Question 54 : D and F are mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB (in cm), if EF = 4.8 cm.

Question 55 : ABC is right angled triangle, right angle at B, $AC=25$, $AB=7$ then BC= ? <br/>

Question 56 : $\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$

Question 57 : 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 58 : 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 59 : 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 60 : 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 61 : $ABCD$ is parallelogram and $P$ isthe mid point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then the ratio $AQ:QC=$

Question 62 : 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 63 : In two similar triangles ABC and PQR, if their corresponding altitudes AD and Ps are in the ratio 4:9, find the ratio of the areas of $\triangle ABC$ and $\triangle PQR$.

Question 64 : If $\triangle ABC$ and $\triangle PQR$ are similar and $\dfrac {BC}{QR} = \dfrac {1}{3}$ find $\dfrac {area (PQR)}{area (BCA)}$

Question 65 : The perimeter of rectangle is $140$ cm. If the sides are in the ratio $3 : 4$, find the lengths of the four sides and the two diagonals

Question 66 : 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 67 : $ABC$ 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 68 : Two isosceles triangles have equal vertical angles and their areas are in the ratio $16:25$. Find the ratio of their corresponding heights.

Question 69 : Given $\Delta ABC-\Delta PQR$. If $\dfrac{AB}{PQ}=\dfrac{1}{3}$, then find $\dfrac{ar\Delta ABC}{ar\Delta PQR'}$.

Question 70 : 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 71 : If the sides of two similar triangles are in the ratio $2 : 3$, then their areas are in the ratio:

Question 72 : The area of two similar triangles are in ratio 16:81. Find the ratio of its sides.

Question 74 : The sides of a triangle are in the ratio 4 : 6 : 7. Then<br>

Question 75 : 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&#160;P, then<br/>$\displaystyle \Delta APB$ is similar to $\displaystyle \Delta CPD.$<br/><br/>

Question 76 : 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>

Question 77 : The altitude of an equilateral triangle of side lenght of $2\sqrt{3}$ cm is:

Question 78 : Instead of walking along two adjacent sides of a rectangular field,a boy book a short - cut along the diagonal of the field and saved a distance equal to 1/2 the longer side. The ratio of the shorter side of the rectangle to the longer side was:.

Question 79 : 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 80 : If all the three altitudes of a triangle are equal, the triangle is equilateral.<br/><b>State whether the above statement is true or false.</b><br/>

Question 81 : In triangle ABC, AD is perpendicular to BC and $AD^{2}\, =\, BD\, \times\, DC.$ Find $\angle BAC$

Question 82 : $\angle BAC$ of triangle $ABC$ is obtuse and $AB=AC$. $P$ is a point in $BC$ such that $PC= 12$ cm. $ PQ $ and $PR$ are perpendiculars to sides $AB$ and $AC$ respectively. If $PQ= 15$ cm and $=9$ cm; find the length of $PB$.<br/>

Question 83 : If $\triangle ABC$ is similar to $\triangle DEF$ such that $BC=3$ cm, $EF=4$ cm and area of $\triangle ABC=54\: \text{cm}^{2}.$ Find the area of $\triangle DEF.$ (in cm$^2$)<br/>

Question 84 : 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 85 : The foot of a ladder is $6$m away from a wall and its top reaches a window $8$m above the ground. If the ladder is shifted in such a way that its foot is $8$m away from the wall, to what height does its top reaches?

Question 86 : If $\Delta ABC \sim \Delta PQR$ and $\displaystyle {{PQ} \over {AB}} = {5 \over 2}$ then area $(\Delta ABC):$ area $(\Delta PQR) = ?$

Question 87 : $\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta DEF$ are two similar triangles such that&#160;$\displaystyle \angle A={ 45 }^{ \circ &#160;},\angle E={ 56 }^{ \circ &#160;}$, then&#160;$\displaystyle \angle C$ =___.<br/>

Question 88 : 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 89 : 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 90 : 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 91 : Two triangles ABC and PQR&#160; are similar, if $BC : CA : AB = $1: 2 : 3, then $\dfrac{QR}{PR}$ is<br/>

Question 92 : If $A={30}^{\circ},\,a=100,\,c=100\sqrt{2}$, find the number of triangles that can be formed.

Question 93 : 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 94 : 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 95 : If two triangles are similar then, ratio of corresponding sides are:

Question 96 : <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 97 : Two equilateral triangles with side $4 \ cm$ and $6 \ cm$ are _____ triangles.

Question 98 : The base of a triangle is $80$, and one of the base angles is $60^{\circ}$. The sum of the lengths of the other two sides is $90$. The shortest side is

Question 99 : 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 100 : A has a pair of triangles corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional,<br>$S_1=A'$s triangles must be similar<br>$S_2=B'$s pentagons must be similar<br>Which of the following statement is correct?

Question 101 : $\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 102 : 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>

Question 103 : 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?