Question

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

Explanation:

Step1: Use the SSS Congruence Theorem

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

Step2: Solve the linear equation

Subtract \(3x\) from both sides: \(3x+6 - 3x=4x - 1-3x\), which gives \(6=x - 1\).
Then add \(1\) to both sides: \(6 + 1=x-1 + 1\).

Answer:

\(x = 7\)