Question

Triangle ABC is translated to create triangle DFG, as shown below.

2y + 12 cm
212y - 3) cm
312x + 10) cm
12x + 12 cm
G
In these triangles, side AB is congruent to side DF, and side BC is congruent to side FG. Determine the values of x
andy
Show your work

Answer 1

`x=3`

`y = 9`

Explanation:

Given

The translated triangles

Required

Find x and y

We have:

`AB = DF`

`BC = FG`

`AB = DF` means:

`3(2x + 10) = 12x + 12`

Open bracket

`6x + 30 = 12x + 12`

Collect like terms

`12x - 6x = 30 -12`

`6x = 18`

Divide by 6

`x=3`

`BC = FG` means

`2y + 12 = 2(2y - 3)`

Open bracket

`2y + 12 = 4y - 6`

Collect like terms

`4y - 2y = 12+6`

`2y = 18`

Divide by 2

`y = 9`