Find the value of the variable that results in congruent triangles. Complete the explanation.

Question

AC is congruent to DF because AC = DF = 9 in. Angle C is congruent to Angle F. EF must correspond to BC. The triangles are congruent by the SAS Triangle Congruence Theorem when x only =

Triangle ABC:

Line Segment AC is 9 inches

Angle C is 30 degrees

CB is 2x inches

Triangle DEF:

Line Segment DF is 9 inches

Angle F is 30 inches

Line segment FE is x+4 inches

.

Answer 1

Since BC = DF and angle C = angle F, we must have BC = EF to have congruent triangles by the side-angle-side (SAS) theorem. Hence:

BC = EF

2x = x + 4

Solve for x.