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ralphmerridew
ralphmerridew
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Alternate answer:

It can only have a side length of 1.

Consider any reflection where A is reflected across B to A'. Before, the area is (AB)(height). After, the area is (A'B)*(height). After, the area is (A'B)*(height'). The reflection keeps (AB) = (A'B), and the two heights are the same, so the area remains the same.

Therefore, only triangles with area equal to that of the original triangle can be formed, and the only equilateral triangle with that area is a congruent one.

Alternate answer:

It can only have a side length of 1.

Consider any reflection where A is reflected across B to A'. Before, the area is (AB)(height). After, the area is (A'B)(height'). The reflection keeps (AB) = (A'B), and the two heights are the same, so the area remains the same.

Therefore, only triangles with area equal to that of the original triangle can be formed, and the only equilateral triangle with that area is a congruent one.

Alternate answer:

It can only have a side length of 1.

Consider any reflection where A is reflected across B to A'. Before, the area is (AB)*(height). After, the area is (A'B)*(height'). The reflection keeps (AB) = (A'B), and the two heights are the same, so the area remains the same.

Therefore, only triangles with area equal to that of the original triangle can be formed, and the only equilateral triangle with that area is a congruent one.

Source Link
ralphmerridew
ralphmerridew
  • 5.3k
  • 18
  • 35

Alternate answer:

It can only have a side length of 1.

Consider any reflection where A is reflected across B to A'. Before, the area is (AB)(height). After, the area is (A'B)(height'). The reflection keeps (AB) = (A'B), and the two heights are the same, so the area remains the same.

Therefore, only triangles with area equal to that of the original triangle can be formed, and the only equilateral triangle with that area is a congruent one.