Question

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 10 centimeters


Which of the following statements about this triangle is true?
A.
More than one triangle exists with the given conditions, and all instances must be right triangles.

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

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

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

Answer 1

Let the measures of the 2 complementary angles be α and β.

α+β are complementary means, their sum is 90°. So the measure of the remaining 3rd angle is 180°-90°=90°.

This means the triangle is a right triangle, with the length of the hypotenuse equal to 10 cm.

let the length of the sides be a and b.

So lisa can draw any right triangle, with sides a and b, such that


`a^(2) + b^(2) = 10^(2)=100`

which means, infinitely many triangles.

Answer:

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