Triangular square numbers

c1+3=415+21=36210+231=441\begin{aligned}& \phantom{c} {\color{#3D99F6} 1} + {\color{#D61F06} 3 }={\color{#20A900} 4 }\\& {\color{#3D99F6}15} + {\color{#D61F06}21}={\color{#20A900}36 } \\ & {\color{#3D99F6} 210} +{\color{#D61F06} 231 }= {\color{#20A900}441}\end{aligned} Gautam desires to form square numbers under addition operation. To do this he added up the two consecutive triangular numbers and found some of the square numbers(above).

Is it true that the sum of two consecutive triangular numbers is always an square number ?

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