Question

M is the midpoint of AD.

Triangles A B M and D C M are connected at point M. Sides A B and C D are congruent. The length of side B M is 3 x + 6 and the length of corresponding side M C is 4 x minus 1.

What value of x will make triangles ABM and DCM congruent?

3
5
7
9

Answer 1

To determine the value of \(x\) that will make triangles \(ABM\) and \(DCM\) congruent, we need to analyze the information we have.

We know that:
- \(AB\) is congruent to \(CD\).
- The lengths of sides \(BM\) and \(MC\) are given as:
- \(BM = 3x + 6\)
- \(MC = 4x - 1\)

For triangle congruence, we need the corresponding sides to be equal. Thus, we need to set \(BM\) equal to \(MC\):

\[
3x + 6 = 4x - 1
\]

Next, we will solve for \(x\):

1. Subtract \(3x\) from both sides:

\[
6 = x - 1
\]

2. Add \(1\) to both sides:

\[
6 + 1 = x
\]
\[
7 = x
\]

Thus, the value of \(x\) that will make triangles \(ABM\) and \(DCM\) congruent is \(x = 7\).

The correct answer is **7**.