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

C. 7

Explanation:

Find the diagram to the question attached. Two congruent triangles has all its sides to be equal. This means that the sides of ΔABM will be equal to that of ΔDCM (SSS rule).

Given

BM = 3x+6

MC =4x-1

Since both triangles are congruent, then BM = MC

Next is to get x;

3x+6 = 4x-1

collect like terms'

3x-4x = -1-6

-x = -7

multiply through by -1

-(-x) = -(-7)

x = 7

Hence the value of x that will make triangles ABM and DCM congruent is 7

Answer 2

7

Explanation:

ΔABM and ΔDCM

4x - 1 = 3x + 6

4x - 3x = 6 + 1

x = 7