# Isosceles Right Triangle

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An isosceles right triangle is the triangle in which along with two equal angles, the third angle in the triangle measures 90º. Isosceles triangle is the triangle in which any two sides of the triangle are equal to each other and the angles opposite to equal sides are also equal. Therefore, the legs of an isosceles right triangle are equal to each other and since the sum of all the angles is 180º, hence the angles are in the form of 45º-45º-90º.

Example 1: Triangle ABC is an isosceles right triangle in which AC is the hypotenuse. If the length of the hypotenuse AC is 10m, then what is the measure of the remaining two sides of the triangle? According to Pythagorean Theorem: AB2 + AC2 = (hypotenuse)2 = AC2

Since triangle ABC is an isosceles right triangle, sides AB = BC and let them be= x

Then x2+ x2= AC2= 102= 100

This gives: 2x2= 100 ==>x2 = 50==> x= √50 = x= 5√2

Therefore, the length of the two sides, AB= BC= 5√2m.

Example 2: Triangle PQR is an isosceles right triangle in which PR is the hypotenuse. If the length of the hypotenuse PR is 14m, then what is the measure of the remaining two sides of the triangle? According to Pythagorean Theorem: PQ2 + QR2 = (hypotenuse)2 = PR2

Since triangle ABC is an isosceles right triangle, sides PQ = QR and let them be= x

Then x2+ x2= AC2= 142= 196

This gives: 2x2= 196==>x2 = 98==> x= √98 = x= 7√2

Therefore, the length of the two sides, PQ= QR= 7√2m.