Refers specifically to the percussion instrument, a metal bar bent into a triangle shape, struck with a beater.
I play the triangle in the orchestra.
Refers to the geometric shape. The native Japanese word 三角形 is more common in everyday and formal contexts; トライアングル is used especially in casual or English-influenced settings, or in compound terms.
See also: 三角形
There was a triangle-shaped chocolate on the desk.
I played the triangle in music class.
I struck the triangle at the conductor's cue.