Lisa is asked to draw a triangle with the following specifications:

two angles are complementary
the side between the two complementary angles has a length of 12 centimeters

Which of the following statements about this triangle is true?

A.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.

B.
More than one triangle exists with the given conditions, and all instances must be right triangles.

C.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.

D.
Exactly one triangle exists with the given conditions, and it must be a right triangle.

Question

06-05-2018
Mathematics

contestada

Lisa is asked to draw a triangle with the following specifications:

two angles are complementary
the side between the two complementary angles has a length of 12 centimeters

Which of the following statements about this triangle is true?

A.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.

B.
More than one triangle exists with the given conditions, and all instances must be right triangles.

C.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.

D.
Exactly one triangle exists with the given conditions, and it must be a right triangle.

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MsEHolt MsEHolt · Answer 1 · 2018-05-16T20:50:14+02:00

B is correct.

Since two of the angles are complementary, adding up to 90°, the third angle must be 180-90=90°.

However, this does not mean only one triangle exists. The only information we are given about the two angles is that they are complementary. This could be 30 and 60; 45 and 45; or multiple other combinations. This means there is more than one triangle that fits these criteria.