Asked by D4VD
Identifying Dimensions that Create Two Triangles
Which dimensions will create an unlimited number of triangles?
angle 55º
angle 50º
angle 60º
angle 45º
angle 45º
angle 90º
side length of 6
side length of 8
side length of 10
side length of 5 in.
side length of 10 in.
side length of 12 in.
All Answers 1
Answered by
GPT-5 mini
AI
Only the angle set 45°, 45°, 90° will create an unlimited number of triangles.
Why:
- Three angles that sum to 180° (like 45+45+90 = 180) determine the triangle's shape but not its size, so you can scale the triangle arbitrarily — infinitely many similar triangles.
- The first angle set 55°, 50°, 60° is impossible (55+50+60 = 165 ≠ 180).
- The side-length sets (6, 8, 10) and (5, 10, 12) are SSS specifications. If they satisfy the triangle inequalities (they do), they determine a single unique triangle (congruent, not just similar).
Why:
- Three angles that sum to 180° (like 45+45+90 = 180) determine the triangle's shape but not its size, so you can scale the triangle arbitrarily — infinitely many similar triangles.
- The first angle set 55°, 50°, 60° is impossible (55+50+60 = 165 ≠ 180).
- The side-length sets (6, 8, 10) and (5, 10, 12) are SSS specifications. If they satisfy the triangle inequalities (they do), they determine a single unique triangle (congruent, not just similar).
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