Construct a triangle with sides congruent to given line segments. Does a solution always exist? How many congruent solutions are there for this problem?

ii. Yes, a solution always exists.

iii. There is only one congruent solution to the problem.

Step-by-step explanation:

Two or more lines are said to be congruent is they have the same length. These lines could be at certain angles to each other, which can be constructed to produce a triangle.

Given line segments, constructing a triangle with sides congruent to the line would produce only one triangle.

See the attachment for an example of the construction.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

sine

step-by-step explanation: