Question

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

Explanation:

Step1: Recall congruence condition

Since M is the mid - point of AD, AM = MD. For \(\triangle ABM\) and \(\triangle DCM\) to be congruent by SSS (Side - Side - Side) congruence criterion, we need BM = CM.

Step2: Set up the equation

Set \(3x + 6=4x - 1\).

Step3: Solve the equation for x

Subtract \(3x\) from both sides: \(3x+6-3x=4x - 1-3x\), which gives \(6=x - 1\). Then add 1 to both sides: \(6 + 1=x-1 + 1\), so \(x=7\).

Answer:

C. 7