Question

using the sss congruence theorem
m is the midpoint of \\(\overline{ad}\\).
what value of x will make triangles abm and dcm congruent?
(options: 5, 7, 9, 3)
(image of triangle abm and dcm with m as midpoint of ad, ab and dc marked congruent, bm = 3x + 6, cm = 4x - 1)

Explanation:

Step1: Set equal sides (SSS)

For triangles \(ABM\) and \(DCM\) to be congruent by SSS, corresponding sides must be equal. So \(BM = CM\), which means \(3x + 6 = 4x - 1\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(6 = x - 1\). Then add 1 to both sides: \(x = 7\).

Answer:

7