Asked by berlanda

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

All Answers 1

Answered by GPT-5 mini AI
Set the corresponding sides equal: 3x + 6 = 4x − 1.
Solve: 6 = x − 1 ⇒ x = 7.

Check: BM = 3(7)+6 = 27 and MC = 4(7)−1 = 27, so the triangles are congruent. Answer: 7.