Question

In the figure, △CBA ~ △DEF, Line segment BG is congruent to line segment GA., and Line segment FH is congruent to line segment HE.. Solve for x.

x = 13 1 over 2

x = 1 5 over 18

x = 16 1 over 2

x = 38 1 over 2

Answer 1

Since the triangles are similar, the lengths of all segments in one triangle are proportional to the corresponding segments in the other triangle. Set up a proportion.

Answer 2

Would the proportion be like lets say 3=3x-2?

Answer 3

No.
Find a segment in the left triangle and its corresponding segment in the right triangle. Write them as a ratio. One over the other in a fraction.

Answer 4

Can you name one segment in the left triangle and its corresponding segment in the right triangle?

Answer 5

A/G and E/H

Answer 6

No. Actually, AG corresponds to HF, but they don't help because we don't know their lengths.
The only segments that can help us are: AC, GC in the left triangle and DH, DF in the right triangle.

Answer 7

Okay now im getting it

Answer 8

There are two segments in the left triangle and two segments in the right triangle that we can use.
Each segment in the left triangle has to correspond to one of the two in the right triangle.

Answer 9

Does AC coreespond to DH or to DF?
Does GC correspond to DH or to DF?

Answer 10

AC to FD and CD to DH

Answer 11

CD?

Answer 12

GC

Answer 13

I think you meant
AC to FD and CG to DH

Answer 14

Right.

Answer 15

Their lengths are proportional. So
AC/FD = CG/DH

Answer 16

Now just substitute each segment name with its length: AC = x + 3; CG = 3; DH = 7; FD = 3x - 2

Answer 17

\[\frac{ x+3 }{3x-2 }=\frac{ 3 }{ 7 }\]

Answer 18

Excellent!

Answer 19

Now you need to solve for x. You have a proportion. You can cross multiply.