select the correct answer. based on these segment lengths, which group of segments can form a triangle? a…

select the correct answer. based on these segment lengths, which group of segments can form a triangle? a. 3, 10, 14 b. 8, 7, 13 c. 3, 2, 5 d. 20, 7, 13

select the correct answer. based on these segment lengths, which group of segments can form a triangle? a. 3, 10, 14 b. 8, 7, 13 c. 3, 2, 5 d. 20, 7, 13

Answer

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option A

$3 + 10=13<14$, so these segments cannot form a triangle.

Step3: Check option B

$8 + 7 = 15>13$, $8+13 = 21>7$, $7 + 13=20>8$. These segments can form a triangle.

Step4: Check option C

$3+2 = 5$, the sum of two sides is equal to the third side, so these segments cannot form a triangle.

Step5: Check option D

$7 + 13=20$, the sum of two sides is equal to the third side, so these segments cannot form a triangle.

Answer:

B. 8, 7, 13