In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

(A) To determine if $\triangle ABC$ is a right triangle,we check if it satisfies the converse of the Pythagoras theorem,which states that if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides,then the triangle is a right triangle.
Given sides are $AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$.
Calculate the squares of the sides:
$AB^2 = 24^2 = 576 \, cm^2$
$BC^2 = 10^2 = 100 \, cm^2$
$AC^2 = 26^2 = 676 \, cm^2$
Now,check the sum of the squares of the two smaller sides:
$AB^2 + BC^2 = 576 + 100 = 676 \, cm^2$
Since $AB^2 + BC^2 = AC^2$ $(576 + 100 = 676)$,the triangle satisfies the Pythagoras theorem.
Therefore,$\triangle ABC$ is a right triangle with the right angle at vertex $B$.