Which dimensions can create more than one triangle? a. three angles measuring 25, 65, and 90 b. three angles measuring 50, 50, and 50 c. three sides measuring 5 in., 12 in., and 13 in. d. three sides measuring 4 ft, 8 ft, and 10 ft

  A.  three angles measuring 25, 65, and 90

Step-by-step explanation:

For any triangle to be formed, the sum of angles must be 180° and the lengths of the sides must satisfy the triangle inequality (the sum of the two shortest sides is at least the length of the longest side).

A triangle can be formed only by selections A, C, and D. The triangles formed by the specification of 3 sides are unique. (That is why we can have SSS congruence.) So selections C and D will not form more than one triangle.

The triangle formed by three given angles (and no given side) will not be unique. (That is why we cannot have AAA congruence; only AAA similarity.) Many different triangles can be formed having these angles.

The appropriate choice is selection A.

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