Question

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

Explanation:

Step1: Use congruent triangle property

Since \(M\) is the mid - point of \(AD\), \(AM = DM\). Also, if \(\triangle ABM\cong\triangle DCM\) (by \(SAS\) congruence criterion, assuming \(AB = DC\) (not shown in the problem but for the sides \(BM\) and \(CM\) to be equal for congruence)), then \(BM=CM\). So, \(3x + 6=4x-1\).

Step2: Solve the equation

Subtract \(3x\) from both sides of the equation \(3x + 6=4x - 1\). We get \(6=x - 1\).

Step3: Find the value of \(x\)

Add \(1\) to both sides of the equation \(6=x - 1\). So, \(x=7\).

Answer:

C. 7