Question

using the sss congruence theorem
m is the midpoint of ad. what value of x will make triangles abm and dcm congruent?
3
5
7
9

Explanation:

Step1: Use the property of midpoint and SSS congruence

Since \(M\) is the midpoint of \(\overline{AD}\), \(AM = DM\). For \(\triangle ABM\) and \(\triangle DCM\) to be congruent by SSS (Side - Side - Side) congruence theorem, \(BM=CM\).
So, we set up the equation \(3x + 6=4x-1\).

Step2: Solve the linear equation

Subtract \(3x\) from both sides of the equation:
\(3x+6-3x=4x - 1-3x\)
\(6=x - 1\)
Add \(1\) to both sides:
\(x=6 + 1\)
\(x = 7\)

Answer:

\(7\)