By triangle inequality the area, Sum of the two sides should be given thus the third side.The differ...

In am isoscles triangle the base angles are equal. Let the vertex angle be x.Then the base angle $=3...

https://clay6.com/mpaimg/942_a.jpgSAS rule holds good only if AC = DE.

https://clay6.com/mpaimg/941_a.jpg $AB = AC (given) $$\implies \angle{B} = \angle{C} $ (angles to th...

In a triangle sum of any two sides should be greater than the third side$x + 8 > 12$$12 + 8 > ...

Area = $\frac{1}{2} \times b \times h$$\implies 180 = \frac{1}{2} \times 40 \times h$ $\implies h = ...

$AB || ED $ and $BC || EF$$\implies \angle{ABC}$ and $\angle{DEF} $ are cointerior angle.$\therefore...

$\angle{AoE} = 5y$ (vertically opposite angles).$\begin{align*} \therefore 2y + 5y +2y &= 180^{...

https://clay6.com/mpaimg/940_a.jpg$\angle{A} + \angle{B} + \angle{C}= 180^{\circ}$$\frac{120}{2} + \...

$\begin{align*}40 + 4x + 3x &= 180^{\circ} \\ \implies 7x & = 140^{\circ} \\ x & = 20^{\...

https://clay6.com/mpaimg/939_a.jpg$\begin{align*} \text{Area of the $\Delta$ ABC} &= \frac{1}{2}...

Sum of two interior opposite angles is equal to one exterior angle (ie) $x + x = 115^{\circ}$ $\impl...

$\angle{x} + \angle{y} + \angle{z} = 180^{\circ}$$x = 3y$ and $x = \frac{z}{2} \implies 2x = z$$\the...

$\angle{A} + \angle{B} + \angle{C}= 180^{\circ}$$\frac{\angle{A} + \angle{B} }{2} = 80^{\circ}$$\beg...

In a triangle sum of the two sides should be greater than the third side $7+5=12$Option :1 Let us ta...

The measures of an isosceles right triangle is in the ratio $x: x: x \sqrt{2}$$\therefore 6 : 6 : 6\...

AE = $3x$ and ED = $x$$\implies$ AD = $4x$ $\implies$ AB = $4x$$\Delta ABE$, $AB^2 + AE^2 = BE^2$$(3...

https://clay6.com/mpaimg/938_a.jpgSince the given area is 3600 sq. feet, the side of the square fiel...

https://clay6.com/mpaimg/937_a.jpg $AB^2 + BC^2 = AC^2$$\begin{align*}10^2 + 5^2 &= 125 \\ &...

https://clay6.com/mpaimg/915_a.jpg $AO^2 + OB^2 = AB^2$$40^2 + 30^2 = AB^2$$1600 + 900 = 2500$$\ther...

If the angles of a right triangle are 45 - 45 - 90, then their sides are in the ratio $x:x:x\sqrt{2}...

When two lines meet at right angles, they are called perpendicular lines.

In a planes lines can be either parallel or intersecting , hence options a and b are correctHence o...

Sum of the length of two sides of a triangle should be greater than the third side.$\therefore$ 7, 1...

$85 + 75 + 20 = 180^{\circ}$Hence they can form a triangle.

Two coplanar angles with a common side, a common vertex, and no common interior points are called ad...

$2x + 4 + 3x + 9 = 90^{\circ}$$\begin{align*} \implies 5x &= 90 - 13 \\ 5x & = 77 \\ \impli...

It can be seen that $\angle{B} = \angle{F}$, $\angle{A} = \angle{F}$ and $AB = EF$. Hence by $ASA$ c...

BC = QRArea of congruent triangles are equal hence area of $\Delta ABC = 24 \;sq. cm$$\frac{1}{2} \t...

$\begin{align*} 7x + 3x+ 4x & = 180^{\circ} \\ \implies 14 x & = 180^{\circ} \\ x & = 1...

$\begin{align*} 70 + 4x + x & =180^{\circ} \; \; \; \text{(angles on the same side of the trans...

$\angle{x} = 40^{\circ}, \; \; \; \; \angle{y} = 35^{\circ}$ (alternate interior angle) $\therefore ...

A parallelogram with side of equal length is called a rhombus.

In a triangle, the exterior angle is equal to the sum of two interior opposite angles.

https://clay6.com/mpaimg/899_a.jpg$\begin{align*} x + y + 65 & = 144 \\ \implies x + y & = 7...

Let the length of each side be $x$ cm.Then its area $= \frac{3}{4} \;x^2$If its side is $x + 2 \;cm ...

Solution :Sum of two co interior angles is $180^{\circ}$$2x + 3x = 180^{\circ}$ (angle on the same s...

The congruent part of the side ED is PR.

Given : $ \angle BCD = \angle ADC$ and $ \angle ACB = \angle BDA$also $CD = CD $$\begin{align*} \the...

https://clay6.com/mpaimg/896_a.jpgSince $\angle R > \angle Q$, $\; \; \;PQ > PR$.Side opposit...

Angles in a regular hexagon $120^{\circ}$$\therefore 6 \times 120^{\circ} = 720^{\circ}$

In $\Delta AOD$ :$\begin{align*} 90 + x + x-6 &= 180^{\circ} \\ \implies 2x - 6 & = 90^{\cir...

https://clay6.com/mpaimg/3_corr24.jpgSince all the three lines are parallel. $125^{\circ}+x=180^{\ci...

https://clay6.com/mpaimg/894_a.jpgThey form a pair of corresponding angles Hence $\angle{2} = 115^{\...

$ a + b = 180^{\circ}$ (linear pair)$ a - b = 100^{\circ} $ (given)$\begin{align*} \therefore 2a &am...

$x + x = 75^{\circ}$ (sum of two interior opposite angles is equal to the exterior angle)$\begin{ali...

$\begin{align*}90 + x + \frac{x}{2} &= 180^{\circ} \\ \frac{3x}{2} & = 90^{\circ} \\ x &...

$\begin{align*} 2x + 3y &= 180^{\circ} \\ 2(30) + 3y &= 180^{\circ} \\ \implies 3y & = 1...

$\begin{align*} Perimeter &= x + x+ 2 + x + 4 \\ 57 & = 3x + 6 \\ \implies 3x & = 51 \\...

The angle of the $\triangle ABC = 30^{\circ}, 60^{\circ}, 90^{\circ}$ Hence the ratio is $x: \sqrt{3...