Right Angled Triangles and Pythagoras Property

The the side of an isosceles right triangle whose hypotenuses is $10 cm$ is $k\sqrt{2}$,value of $k$ is _____

The hypotenuses of an isosceles right triangle whose side is $5 cm$

For a triangle $∆ABC$, $\angle ABC=90°$, $\angle BAC=\angle BCA=45°$. Find the relation between $AB$ and $BC$

A triangle with three angles $90°,45°$ and $45°$ is known as right _____ triangle

The triangle $∆ABC$ with $\angle ABC=90°$ and $AB=BC$ is a _____ triangle.

Find the other angles of the triangle with $\angle ABC=90°$ and $AB=BC$

State True or False

The hypotenuses of an isosceles right triangle whose side is $6 cm$ is $12 cm$.

An isosceles right triangle has angles of $45°,45°$ and $90°$.

In $△DEF$, if $\angle E=90°$. If $\angle D+\angle F$ is $k°$, find the value of $k$.

A ladder $13$m long rests against a vertical wall. If the foot of the ladder is $5$ m from the foot of the wall, find the distance of the other end of the ladder from the ground.

ABC is a right angled triangle. $\angle ABC={90}^0, AC=25cm$ and $AB=24 cm.$ Calculate the area of $△ABC.$

AD is drawn perpendicular to BC, the base of an equilateral triangle ABC. Given $BC=10 cm,$ find the length of AD, correct to $1$place of decimal.

All the angles of the right angled triangle are equal to $90°$.

P is a point in the interior of a rectangle ABCD. If P is joined to each of the vertices of the rectangle and the lengths PA, PB and PC are  $3 cm, 4 cm and 5 cm$ respectively, find the length of PD.

In Fig. $10.34,\angle B$ is acute angle and  $AD\perp BC.$Show that,

$b^2=a^2+c^2-2ax$

In Fig. $10.34,\angle B$ is acute angle and  $AD\perp BC.$Show that,

$b^2=h^2+a^2+x^2-2ax$

In $△ABC, \angle B={90}^0$ and D is the mid point of BC. Prove that $B{C}^2=4(A{D}^2-A{B}^2)$

In $△ABC, \angle B={90}^0$ and D is the mid-point of BC. Prove that  $A{C}^2=A{D}^2+ 3 C{D}^2$

In $△ABC, \angle A = {90}^0.$ $D$ is the mid point of $AC$. Prove that $B{C}^2-B{D}^2=3 A{D}^2.$

In a right $△ABC,$ right angled at C, P and Q are points on the sides CA and CB respectively dividing those sides in the ratio $2 : 1 .$

Prove that $9 \left(A{Q}^2+P{B}^2\right) = 13 A{B}^2.$