To determine the lengths of AB and BD, we can see that AB is -4 and BD is -1 on the number line. Since the lengths of the sides of a triangle cannot be negative, we take the absolute value of these lengths to get 4 and 1, respectively.
Now, using the Triangle Inequality Theorem, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, to find the possible combinations for the third side, we can add the lengths of the two given sides (AB and BD) and compare with the length of the remaining sides on the number line.
Adding 4 and 1 together gives us 5. Comparing this sum with the remaining lengths on the number line:
- AB + BC = -4 + 3 = -1 (abs value = 1)
- AD + BD = 3 + (-1) = 2 (abs value = 2)
- BC + CD = 3 + 4 = 7
- AC + CD = 3 + 4 = 7
Therefore, the two possible answers that satisfy the Triangle Inequality Theorem are:
BC and AD
A
-4
B
-1
C
3
D
4
A trangle has no congruent sides. The lengths of two sides of the triangle are AB and BD. Use the number line above to determine the lengths of AB and BD. 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)
BC and AD
BC and CD
AC and BC
OCD and AC
Explain
1 answer
11 answers