Question

PLEASEEEE ASAPPPPPP

Find all values of x that make the triangles congruent. Explain your reasoning.

Answer 1

The values of x that make the triangles congruent.

x = 6 and x = 3

Explanation:

Given

• AC = 5x-2

• DC = 3x+10

• AB = 5x

• DB = 4x+3

Given that the triangles are congruent.

According to the SAS (Side-Side-Side)

AC = DC

AB = DB

so

AC = DC

substituting AC = 5x-2 and DC = 3x+10

5x-2 = 3x+10

5x-3x = 10+2

2x = 12

divide both sides by 2

2x/2 = 12/2

x = 6

and

AB = DB

substituting AB = 5x and DB = 4x+3

5x = 4x+3

5x-4x = 3

x = 3

Therefore, the values of x that make the triangles congruent.

x = 6 and x = 3