Which dimensions can create more than one triangle? A. Three angles measuring 75°,45°, and 60°. B. 3 sides measuring 7, 10, 12? C. Three angles measuring 40,50, and60°? D. 3 sides measuring 3,4, and 5

Question

Mathematics

Jenna Mclean

9 July, 21:32

Which dimensions can create more than one triangle? A. Three angles measuring 75°,45°, and 60°. B. 3 sides measuring 7, 10, 12? C. Three angles measuring 40,50, and60°? D. 3 sides measuring 3,4, and 5

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Answers (1)

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Casper · Answer 1

This is vague. Any dimensions that make a triangle can make more than one, just draw another right next to it. What's really being asked is which dimensions can make more than one non-congruent triangle.

A. Three angles measuring 75°,45°, and 60°.

That's three angles, and 75+45+60 = 180, so it's a legit triangle. The angles don't determine the sides, so we have whole family of similar triangles with these dimensions. TRUE

B. 3 sides measuring 7, 10, 12?

Three sides determine the triangles size and shape uniquely; FALSE

C. Three angles measuring 40 °, 50°, and 60°?

40+50+60=150, no such triangle exists. FALSE

D. 3 sides measuring 3,4, and 5

Again, three sides uniquely determine a triangle's size and shape; FALSE