Pythagoras Theorem

Of all the line segments that can be drawn to a given line from a given point outside it, the______is the shortest.

If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is______.

In a $∆ABC$, $\angle B=35°$ and  $\angle C=55°$. Check whether the following is true: 

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

In a $∆ABC$, $\angle B=35°$ and  $\angle C=55°$. Check whether the following is true: 

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

The lengths of the sides of triangles are $a=9 \mathrm{cm}$, $b=12 \mathrm{cm}$ and $c=16 \mathrm{cm}$. Check whether it is right-angle triangle?

The lengths of the sides of triangles are $a=10 \mathrm{cm}$, $b=24 \mathrm{cm}$ and $c=26 \mathrm{cm}$. Check whether it is right-angle triangle? 

In a right triangle, the square of the hypotenuse is equal to the______of the squares of the other two sides.

Find the perimeter of a rhombus, the lengths of whose diagonals are $16 \mathrm{cm}$ and $30 \mathrm{cm}$.

Find the perimeter of the rectangle whose length is $40 \mathrm{cm}$ and a diagonal is $41 \mathrm{cm}$.

Find the length of diagonal of the rectangle whose sides are $16 \mathrm{cm}$ and $12 \mathrm{cm}$.

A man goes $3 \mathrm{km}$ due north and then $4 \mathrm{km}$ due east. How far is he away from his initial position?

A man goes $35 \mathrm{m}$ due west and then $12 \mathrm{m}$ due north. How far is he from the starting point?

Two poles, $18 \mathrm{m}$ and $13 \mathrm{m}$ high, stand upright in a playground. If their feet are $12 \mathrm{m}$ apart, find the distance between their tops.

A tree is broken by the wind but does not separate. If the point from where it breaks is $9 \mathrm{m}$ above the ground and its top touches the ground at a distance of $12 \mathrm{m}$ from its foot,  find out the total height of the tree before it broke.

A $5 \mathrm{m}$ long ladder when set against the wall of a house reaches a height of $4.8 \mathrm{m}$. How far is the foot of the ladder from the wall?

A $15m$-long ladder is placed against a wall to reach a window $12 m$ high. Find the distance of the foot of the ladder from the wall.

In a $∆ABC$, $\angle B=35°$ and  $\angle C=55°$. Check whether the following is true: 

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

The lengths of the sides of triangles are $a=15 \mathrm{cm}$, $b=20 \mathrm{cm}$ and $c=25 \mathrm{cm}$. Check whether it is right-angle triangle?

In right $∆ABC$, the lengths of its legs are given as $a = 6 cm and b = 4.5 cm$. Find the length of its hypotenuse.

The sides of a triangle measure $15 \mathrm{cm}$, $36 \mathrm{cm}$ and $39 \mathrm{cm}$. Show that it is a right-angled triangle.