In an isosceles triangle in addition to two sides being congruent, the base angles, that is the angles formed on the third side are also congruent. That makes the angles made by the legs on the hypotenuse are congruent. Since the vertex angle is a right angle, the sum of the measures of the base angles in a right isosceles triangle is 90
^{o}.
Hence the measure of each of the non right angle is 45
^{0}.
The measure of each of the non right angles in a right isosceles triangle is 45
^{o}.
How are the legs and hypotenuse related in a right isosceles triangle?
The Pythagorean Theorem also known as right triangle formula gives the equation satisfied by the sides of all right triangles
In a right triangle sum of the squares on the legs is equal to the square on the hypotenuse.
c^{2} = a^{2} + b^{2}
where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse.
In a right triangle sum of the squares on the legs is equal to the square on the hypotenuse.
c
^{2 }= a
^{2} + b
^{2} = 2a
^{2} → c= $\sqrt{2a^2}$
where ‘a’ and b’ are the lengths of the legs and c is the length of the hypotenuse.
c=$\sqrt{2a}$
Isosceles right triangle formula:
The right isosceles triangle is also known as a 45, 45, 90 special right triangle indicating the measures of the angles.
The ratio of sides opposite to the respective angles in a right isosceles triangle is 1:1:$\sqrt{2}$
The example given demonstrates the configuration of a right isosceles triangle both in terms of angles and side lengths
Length of the hypotenuse $\sqrt{2}$ x length of the leg.