To determine if an isosceles triangle is a right triangle, we need to consider the relationship between the sides according to the Pythagorean theorem. In an isosceles right triangle, the two equal sides are the legs, and the longest side is the hypotenuse.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse [tex]\( c \)[/tex] is equal to the sum of the squares of the lengths of the other two sides, which are equal in this case.
Given:
- [tex]\( c \)[/tex] is the longest side (hypotenuse)
- [tex]\( a \)[/tex] are the other two equal sides (legs)
According to the Pythagorean theorem:
[tex]\[ a^2 + a^2 = c^2 \][/tex]
Simplifying the left-hand side:
[tex]\[ 2a^2 = c^2 \][/tex]
Hence, the correct equation to determine if the triangle is a right triangle is:
[tex]\[ 2a^2 = c^2 \][/tex]
So, the correct equation is:
[tex]\[ 2a^2 = c^2 \][/tex]
