Question 1 :
<p class="wysiwyg-text-align-left">&#160;State the congruency of following pairs of triangles.</p><p class="wysiwyg-text-align-left">In $\Delta\,ABC$ and $\Delta PQR $, $BC = QR, $&#160;$\angle\,A\,=\,90^{\circ}, \, \angle \,C \,=\,\angle R = 40^{\circ} $ and $ \angle\, Q \,=\,50^{\circ}$.</p>

Question 2 :
State true or false:<br/>If two sides and an angle of a triangle are respectively equal to two sides and an angle of another triangle the two triangles are congruent.&#160;

Question 3 :
In $\Delta ABC$, AB = AC and AD is perpendicularto BC. State the property by which $\Delta ADB\, \cong\,\Delta ADC$.

Question 4 :
If $\triangle$ $ABC$ $\cong$ $\triangle$ $PRQ$, then $\angle$ $B$ and $PQ$ are respectively equal to

Question 5 :
If the two sides and the ____ angle of one triangle are respectively equal to two sides and the included angle of the other triangle, then the triangles are congruent.

Question 6 :
In $\triangle ABC$ and $\triangle DEF$, $AB = FD$ and $\angle A = \angle D.$ The two triangles will be congruent by $SAS$ axiom, if:<br/>

Question 7 :
State true or false:<br/>In parallelogram&#160;$&#160;ABCD&#160;$.$&#160;E&#160;$&#160;and&#160;$&#160;F $&#160;are mid-points of the sides&#160;$&#160;AB&#160;$&#160;and&#160;$&#160;CD&#160;$&#160;respectively. The line&#160;segments&#160;$&#160;AF&#160;$&#160;and&#160;$&#160;BF&#160;$&#160;meet the line segments&#160;$&#160;ED&#160;$&#160;and &#160;$&#160;EC&#160;$&#160;at points&#160;$&#160;G&#160;$&#160;and&#160;$&#160;H&#160;$&#160;respectively, then$&#160;GEHF&#160;$&#160; is a parallelogram.&#160;

Question 8 :
It is given that $\triangle ABC\cong \triangle FDE$ and $AB=\,5cm$, $\angle B={ 40 }^{ 0 }$ and $\angle A={ 80 }^{ 0 }$. Then which of the following is true?

Question 10 :
For&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta DEF$,&#160;$\displaystyle \angle B=\angle D,\angle C=\angle F$ and $BC=DF$. Therefore which of the following is correct?

Question 12 :
In $\Delta ABC, \angle B = 30^{\circ}, \angle C = 80^{\circ}$ and $\angle A = 70^{\circ}$ then,<br>

Question 13 :
Angles opposite to ____ sides of an isosceles triangles are equal.

Question 14 :
If in a$\displaystyle \Delta ABC, \angle A=60^{\circ}$ and AB = AC then$\displaystyle \Delta ABC $ is__

Question 15 :
In a triangle ABC, $\angle B = \angle C = 45^o$, then the triangle is ........................

Question 16 :
Assertion: Show that the points $(a, a), (-a, -a)$ and $(-\sqrt{3}a, \sqrt{3}a)$ are the vertices of an equilateral triangle.&#160; Reason: Using the distance formula we can show that the sides are equal.

Question 17 :
In a $\Delta$ $PQR$, $PQ = PR$ and $\angle{Q}$ is twice that of&#160;$\angle{P}$&#160;. Then $\angle{Q}$ =

Question 19 :
If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by

Question 20 :
A point within an equilateral triangle, where perimeter is $18$ m, is $1$ m from one side and $2$ m from another side. Its distance from the third side is:<br/>

Question 21 :
Which of the following sets of side lengths will not form a triangle?

Question 22 :
The sides of a triangle are $50\ cm,\ 78\ cm$ and $112\ cm$. The smallest altitude is....

Question 23 :
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 24 :
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 26 :
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 27 :
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 28 :
The triangle obtained by joining the points A(-5, 0) B(5, 0) and C(0, 6) is

Question 29 :
In an equilateral triangle if 3 times the squareof one side is equal to K times the square ofits altitude then K equals

Question 30 :
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