Question

Using the SSS congruence theorem, M is the midpoint of AD. Triangles ABM and DCM are connected at point M. Sides AB and CD are congruent. The length of side BM is 3x+6 and the length of the corresponding side MC is 4x−1. What value of x will make triangles ABM and DCM congruent?

a) 3
b) 5
c) 7
d) 9

Answer 1

To make triangles ABM and DCM congruent, the lengths of BM and MC must be equal. By setting the two expressions 3x+6 and 4x-1 equal to each other and solving for x, we find that the value of x is 7.

Step-by-step explanation:

Using the SSS congruence theorem, we are told that M is the midpoint of AD and that triangles ABM and DCM are connected at point M. It is given that sides AB and CD are congruent, and we have the lengths of BM as 3x+6 and MC as 4x-1. To make triangles ABM and DCM congruent, the lengths of BM and MC must also be equal, since M is the midpoint of AD. Setting the lengths of BM and MC equal to each other:

3x + 6 = 4x - 1

Solving for x, we get:

x = 7

Therefore, the value of x that will make triangles ABM and DCM congruent is 7.