Question 1 :
If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by
Question 3 :
Which of the following sets of side lengths form a triangle?
Question 4 :
Find the perimeter of an isosceles right triangle with each of its congruent sides is $7\,cm$.
Question 5 :
A right triangle has angles which measure $30, 60$ and $90$ degrees. If the perimeter of this triangle is $15 +$ $\displaystyle 5\sqrt{3}$, then the length of the hypotenuse of this triangle is
Question 8 :
Which of the following cannot be the sides a right angle triangle?<br>
Question 9 :
Say true or false.<br/>In a $\Delta ABC,  \angle C=3  \angle B=2 (\angle A + \angle B)$, then angles are $20^{\circ}, 40^{\circ}, 100^{\circ}.$
Question 10 :
Can we construct sets of Pythagorean Triples with all even numbers?
Question 12 :
Which one of the following combinations of given parts does not determine the shape and size of indicated triangle?
Question 14 :
Find the altitude of an equilateral triangle of side $5\sqrt 3cm$
Question 16 :
In a triangle $ ABC $, $ AB= AC $ and $ \angle A= 36^{\circ} $. If the internal bisector of $ \angle C $ meets $ AB $ at point $ D $, then
Question 17 :
Which side is the hypotenuse for the sides, $89, 39$ and $80$ in a right angled triangle? (Apply Converse of Pythagoras theorem).<br/>
Question 18 :
Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$
Question 19 :
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is<br>
Question 20 :
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 21 :
State true or false:<br/>Sum of the three angles of a triangle is $180^o$.<br/>
Question 22 :
If two sides of an isosceles $\Delta$ Ie are $3$ cm and $8$ cm, then the length of the third side is
Question 23 :
In a right angled triangle the square of the hypotenuse is twice the product of the square of the other sides. Then the triangle is<br>
Question 24 :
State true or false:The bisectors of the base angles of an isosceles triangle are equal.
Question 25 :
Which of the following could be the side lengths of a right triangle?
Question 26 :
Measures of angles of a triangle are x, 2x, 3x (all in degrees). What type of triangle it is?
Question 28 :
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 29 :
In a $\Delta$ $PQR$, $PQ = PR$ and $\angle{Q}$ is twice that of $\angle{P}$ . Then $\angle{Q}$ =
Question 30 :
The area of an isosceles triangle is $9 cm^2$. If the equal sides are $6 cm$ each in length, then the angle between them is
Question 31 :
The vertical angle of an isosceles triangle measure $(5t-18)^{o}$ and one of the base angles measure $3t^{o}$. The value of $t$ is
Question 32 :
If length of the largest side of a triangle is 12 cm then other two sides of triangle can be :<br>
Question 34 :
It is not possible to construct a triangle with which of the following sides?<br/>
Question 35 :
In $\Delta PQR$, PE is perpendicular bisector of $\angle QPR$, then :
Question 36 :
Write the measure of each angle of an isosceles right-angled triangle.
Question 37 :
What is the length of the hypotenuse formed if the two sides are of 5 cm, 12 cm?
Question 38 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 39 :
Angles opposite to ____ sides of an isosceles triangles are equal.
Question 40 :
Find the length of the altitude of an equilateral triangle, each side measuring $'a'$ units.
Question 41 :
The sides of a triangle (in cm) are given below: In which case, the construction of $\triangle $ is not possible?<br/>
Question 42 :
If one angle of a $\Delta$ is equal to the sum of the other two, the triangle is<br>
Question 43 :
If two vertices of an equilateral triangle be $(0, 0)$ and $(3, \sqrt {3})$, then the third vertex is _________.
Question 46 :
In a triangle ABC, if BC=AB and $\angle C={ 80 }^{ 0 }$ then $\angle B =$ $.....$
Question 47 :
In $\Delta ABC$, if $\angle A = 35^{\circ}$ and $\angle B = 65^{\circ}$, then the longest side of the triangle is :<br>
Question 48 :
The vertical angle of an isosceles triangle is $15^{\circ}$ more than each of its base angles. What is the vertical angle?
Question 49 :
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 50 :
Sum of any two angles of a triangle is always greater than the third angle.
Question 51 :
Let $O = (0, 0)$; let $A$ and $B$ be points respectively on x-axis and y-axis such that $\angle OBA = 60^{\circ}$. Let $D$ be a point in the first quadrant such that $OAD$ is an equilateral triangle. Then the slope of $DB$ is
Question 52 :
The construction of a triangle $ABC$, given that $BC =$ $6$ cm, $B =$ $45 ^{\circ}$ is not possible when difference of $AB$ and $AC$ is equal to:<br/>
Question 53 :
Which of the following sets of side lengths will not form a triangle?
Question 54 :
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 55 :
Which of the following triplets cannot be the angles of a triangle?
Question 56 :
An equilateral triangle is cut from its three vertices to form a regular hexagon. The percentage of area wasted is
Question 57 :
Triangle ABC is right -angled at C. Find $AC, $ If $AB = 2.2 \ cm\,\, $and$\,\, BC = 1.8 \ cm$.<br/>In each case, answer correct to two place of decimal.
Question 58 :
Which of the following can be the length of the third side of triangle whose two sides measure $18 cm$ and $14 cm $?
Question 59 :
If the area of an equilateral triangle is $25\sqrt{3}$ sq. cms, then find its side.
Question 60 :
The sides of a triangle are $50\ cm,\ 78\ cm$ and $112\ cm$. The smallest altitude is....
Question 61 :
In a $\Delta$ABC, if $\angle A = 40^\circ$ and $\angle B = 55^\circ$ then $\angle C$ is
Question 62 :
In $\Delta\, ABC$, if $AB = BC$ and $\angle\, B\, =\, 80^{\circ},$ then $\angle C\, =$ 
Question 63 :
The sides of a triangle $ABC$ are positive integers. The smallest side has length $l$. What of the following statements is true?
Question 64 :
Out of isosceles triangles with sides of 7 cm and a base with the length expressed by whole number, the triangle with the greatest perimeter was selected. This perimeter is equal to.......
Question 65 :
Two poles of heights $3$m and $18$m are standing on a plane ground. If the distance between the feet of the poles is $36$m, find the distance between their tops.
Question 66 :
The sides of a right triangle are $(x-1)$, $x$ and $(x+1)$. Find the sides of the triangle.
Question 67 :
In a right angled triangle the square of the hypotenuse is twice the product of the square of the other sides. Then the triangle is
Question 68 :
Find all possible lengths of the third side, if sides of a triangle have $3$ and $9$.<br/>
Question 69 :
One of the two equal angles of isosceles triangle are $35^{o}.$ Find the measure of the vertex angle.<br/>
Question 70 :
Assertion: $ABC$ is an isosceles right triangle, right angled at $C$, then $AB^2=3\:AC^2$.
Reason: In an isosceles triangle $ABC$, if $AC=BC$ and $\:AB^2=2\:AC^2$, then $\:\angle C=90^o$.
Question 71 :
The sides of a triangle are $3x+4y,4x+3y$ and $5x+5y$ unit where $x,y> 0$. The triangle is
Question 72 :
If a $\triangle PQR$ is constructed taking QR = $5$ cm, PQ = $3$ cm and PR = $4$ cm, then the correct order of the angles of the triangle is:
Question 73 :
Which is the greatest side in the following triangle?<br>$\displaystyle \angle A:\angle B:\angle C=4:5:6$
Question 74 :
A straight line segment of length <b>'K'</b> moves with its ends on the axes. Find the locus of <b>P</b> which divides the segment on the ratio <b>1:2</b>.<br>
Question 76 :
AB is a straight road leading to C, the foot of a tower. A is at a distance 200 metres from C and B at 75 metres from C. If the angle of elevation of the tower at B be double the angle ofelevation at A, then the height of the tower is<br><br>
Question 77 :
The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. Length of its side is
Question 78 :
Two equal forces act on a particle then the angle between them when the square of their resultant is equal to three times their product is :
Question 79 :
Which of the following statements are true (T) and which are false(F) :<br/>If the altitude from one vertex of a triangle bisects the opposite side, then the <br/>triangle will be isosceles.
Question 80 :
One vertex of an equilateral triangle is $(2, 2)$ and its centroid is $\left (\dfrac {-2}{\sqrt {3}}, \dfrac {2}{\sqrt {3}}\right )$ then length of its side is
Question 81 :
Sum of two sides of a triangle is greater than or equal to the third side.
Question 82 :
The length of two sides of a triangle are $20 $ mm and $29 $ mm. Which of the following can be the value of third side to form the triangle?
Question 84 :
If two vertices of an equilateral triangle have integral coordinates, then the third vertex will have: 
Question 85 :
If a triangle $PQR$ has been constructed taking $QR = 6 $ cm, $PQ = 3 $ cm and $PR = 4 $ cm, then the correct order of the angle of triangle is
Question 86 :
The number of triangles with any three of the length $1, 4, 6$ and $8 $ cm as sides is:
Question 87 :
Write True or False in each of the following . Give reason for your answer:<br>A triangle can be constructed in which AB = $ 5\,cm , \angle $ A = $ 45^{\circ} $ and BC + AC = $ 5\,cm $ .
Question 88 :
If the points $P (12, 8) , Q (-2, a )$ and $R (6, 0)$ are the vertices of a right angled triangle $PQR$, where $\displaystyle \angle R=90^{\circ},$ then the value of $a$ is:
Question 89 :
The side of an equilateral triangle is $20\sqrt 3 cm$. The numerical value of the radius of the circle circumscribing the triangle is:
Question 90 :
A triangle formed by the sides of lengths $4.5cm,6cm,$ and $4.5 cm$ is
Question 91 :
If the smallest number in a Pythagorean triplet is $14$. Find the other two numbers.
Question 92 :
An equilateral triangle has one vertex at (0, 0) and another at $(3 , \sqrt 3)$. What are the coordinates of the third vertex?
Question 93 :
It is possible to have a triangle in which each angle is less than $60^{o}$
Question 94 :
If one angle of a triangle is equal to half the sum of the other two equal angles, the triangle is 
Question 95 :
The difference between the length of any two sides of a triangle is smaller than the length of third side.
Question 96 :
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is
Question 97 :
The height of an equilateral triangle whose side is 6 cm is _____ (in cm)<br><br>
Question 98 :
In a $\Delta\, PQR$, if $PQ = PR$ and $\angle\, Q$ is twice that of $\angle\, P$, then $\angle\, Q\, =$
Question 99 :
If length of two sides of a triangle are $6 \,cm$ and $10 \,cm$, then the length of the third side can be
Question 100 :
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 101 :
The product of the arithmetic mean of the lengths of the sides of a triangle and harmonic mean of the lengths of the altitudes of the triangle is equal to
Question 102 :
The points $O(0, 0), A(\cos \alpha, \sin \alpha)$ and $B(\cos \beta, \sin \beta)$ are the vertices of a right-angled triangle if
Question 103 :
The measures of the angles of $\triangle QRS$ are $m\angle Q = 2x + 4, m\angle R = 4x - 12,$ and $m\angle S = 3x+8.$ $QR = y + 9, RS = 2y-7$, and $QS = 3y-13.$ The perimeter of $\triangle QRS$ is:<br/>
Question 104 :
If the points $( 0,0 ) , ( 3 , \sqrt { 3 } ) , ( p , q )$ form an equilateral triangle and $q _ { 1 } , q _ { 2 }$ are the twovalues of $q$ then $q _ { 1 } + q _ { 2 } =?$
Question 105 :
In $\displaystyle \Delta ABC,$ segments $AD, BE$ and $CF$ are the altitudes. If $AB \times AC = 28.80$ and $BE \times CF = 20,$ then $AD \times BC$ equals:
Question 106 :
In an equilateral triangle if 3 times the squareof one side is equal to K times the square ofits altitude then K equals
Question 107 :
In an isosceles triangle $A B C , A B = A C = 25 \mathrm { cm }$ and $B C = 14$ cm The measure of an altitude from $A$ on BC in $cm$ is
Question 108 :
One of the vertices of an equilateral triangle is $(2, 3)$ and the equation of its opposite side is $x+y-2=0$. The area of triangle is?
Question 109 :
On the sides of an arbitrary triangle ABC, triangles BPC, CQA, and ARB are externally erected such that<br/>$\angle{PBC}=\angle{CAQ}=45^{\circ}$,<br/>$\angle{BCP}=\angle {QCA}=30^{\circ}$,<br/>$\angle{ABR}=\angle{BAR}=15^{\circ}$;<br/>
Question 110 :
$\Delta$ABC is an equilateral triangle of side $2\sqrt 3$cms, P is any point in the interior of $\Delta$ABC. If x, y, z are the distances of P from the sides of the triangle, then $x+y+z=$
Question 111 :
A string of length $12$cm is bent first into a square $PQRS$ and then into an isosceles triangle $PQT$ by keeping the side $PQ$ of the square as base then what is area of the square $PQRS$: area of the triangle $PQT =$
Question 112 :
In an isosceles triangle $A B C , A B = A C = 25 \mathrm { cm }$ and $B C = 14$ cm The measure of an altitude from $A$ on BC in $cm$ is
Question 113 :
The triangle obtained by joining the points A(-5, 0) B(5, 0) and C(0, 6) is
Question 114 :
If the points $( 0,0 ) , ( 3 , \sqrt { 3 } ) , ( p , q )$ form an equilateral triangle and $q _ { 1 } , q _ { 2 }$ are the twovalues of $q$ then $q _ { 1 } + q _ { 2 } =?$
Question 115 :
The radii of described circle of $\triangle {ABC}$ are ${r}_{1}, {r}_{2}$ and ${r}_{3}$ respectively (opposite to vertices $A,B$ and $C$). If ${r}_{2}+{r}_{3}=2R$ and ${r}_{1}+{r}_{2}=3R$ then
Question 117 :
Given an isosceles triangle, whose one angle is $\displaystyle 120^{\circ}$ and radius of its incircle is $\displaystyle  \sqrt{3}$ unit. Then the area of the triangle in sq. units is 
Question 118 :
The radii of described circle of $\triangle {ABC}$ are ${r}_{1}, {r}_{2}$ and ${r}_{3}$ respectively (opposite to vertices $A,B$ and $C$). If ${r}_{2}+{r}_{3}=2R$ and ${r}_{1}+{r}_{2}=3R$ then
Question 119 :
If $(2,4) , (4,2)$ are the extremities of the hypotenuse of right angled isosceles triangle, then the third vertex is
Question 120 :
A string of length $12$cm is bent first into a square $PQRS$ and then into an isosceles triangle $PQT$ by keeping the side $PQ$ of the square as base then what is area of the square $PQRS$: area of the triangle $PQT =$
