A triangle has no congruent sides. The lengths of two sides of the triangle are and
. Use the number line above to determine the lengths of and . Then, use the
Triangle Inequality Theorem to determine which two segments have lengths that could be
used as the third side of the triangle. Select a response containing 2 possible answers.
(1 point)
AB
BD AB BD
BC and AD
CD and AC
AC and BC
BC and CD
Based on the given information, we know that the lengths of two sides of the triangle are not congruent. Looking at the number line, we can see that AB is shorter than BD. Therefore, we can determine that AB is shorter than BD.
Using the Triangle Inequality Theorem, we know that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Possible answer choices could be:
AC and BC: The length of AC + BC > AB
BC and CD: The length of BC + CD > BD
So, the correct answer is:
AC and BC
BC and CD
which one is correct
there is only one answer
Apologies for the mistake in my response. The correct answer is:
AC and BC: The length of AC + BC > AB
This satisfies the Triangle Inequality Theorem, as the sum of the lengths of AC and BC must be greater than the length of AB for them to form a valid triangle.