Pythagoras Theorem

$ABC$ is an isosceles triangle right-angled at $C$. Prove that $A{B}^2=2A{C}^2$.

In the figure, $AD\perp BC, AB=15 \mathrm{cm}, CD=5 \mathrm{cm}$ and $AC=13 \mathrm{cm}$. Calculate the lengths of sides $AD$ and $BC$.

In a right-angled triangle, the sum of the squares of two legs is equal to the square of the _____.

$(5, 12, 13)$ is a Pythagorean triplet

If $x, y$ and $z$ are base, perpendicular and hypotenuse of a right triangle respectively, then according to the Pythagoras Theorem, we get

In the given figure, $ABCD$ is a rhombus in which $AC=16 \mathrm{cm}$ and $BD=12 \mathrm{cm}$. The perimeter of the rhombus is

A person goes $12 \mathrm{m}$ due east and then $5 \mathrm{m}$ due north. The distance from the starting point is

In the figure, $ABC$ is a right triangle right-angled at $B$. The length of $AC$ is

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. Then, $A{B}^2+B{C}^2=A{C}^2$

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. Then, $A{B}^2+A{C}^2=B{C}^2$.

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. State which of the following is/are 'True'.

$A{C}^2+B{C}^2=A{B}^2$

The sides of a triangle are given below. Determine if it is a right triangle:

$a=5 \mathrm{cm}, b=8 \mathrm{cm}, c=11 \mathrm{cm}$

The sides of a triangle are given below. Determine if it is a right triangle:

$a=6 \mathrm{cm}, b=8 \mathrm{cm}, c=10 \mathrm{cm}$

If $a, b, c$ are the three positive integers, then which of the following is true for Pythagorean triplets?

The perpendicular length of a right triangle, whose hypotenuse is $15 \mathrm{cm}$ and base is $12 \mathrm{cm}$, is

The length of the hypotenuse of a right triangle, whose other two sides are $3 \mathrm{cm}$ and $4 \mathrm{cm}$, is