State whether the following statement is True or False. Justify your answer.
If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square,then the area of the triangle also equals the area of the square.
If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square,then the area of the triangle also equals the area of the square.
(TRUE) The statement is True.
According to Euclid's first axiom: 'Things which are equal to the same thing are equal to one another.'
Let the area of the triangle be $A_1$,the area of the rectangle be $A_2$,and the area of the square be $A_3$.
Given: $A_1 = A_2$ and $A_2 = A_3$.
Since both $A_1$ and $A_3$ are equal to the same quantity $A_2$,it follows that $A_1 = A_3$.
Therefore,the area of the triangle is equal to the area of the square.
According to Euclid's first axiom: 'Things which are equal to the same thing are equal to one another.'
Let the area of the triangle be $A_1$,the area of the rectangle be $A_2$,and the area of the square be $A_3$.
Given: $A_1 = A_2$ and $A_2 = A_3$.
Since both $A_1$ and $A_3$ are equal to the same quantity $A_2$,it follows that $A_1 = A_3$.
Therefore,the area of the triangle is equal to the area of the square.
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