To make the given triangles congruent the corresponding sides need to be equal.
Corresponding sides:
GB and HR
BT and RA
GT nad HA
[tex]\begin{gathered} 2x+11=3x-8 \\ \\ 4x+8=5x-11 \\ \\ 4x-11=2x+27 \end{gathered}[/tex]
Use one of the equations above to find x, and then prove if that value you find makes truth all three equations:
Use the first equation:
[tex]\begin{gathered} 2x+11=3x-8 \\ 2x-3x=-8-11 \\ -x=-19 \\ x=19 \end{gathered}[/tex]
Prove if x=19 makes truth the three equations:
First equation:
[tex]\begin{gathered} 2(19)+11=3(19)-8 \\ 38+11=57-8 \\ 49=49 \end{gathered}[/tex]
Second equation:
[tex]\begin{gathered} 4(19)+8=5(19)-11 \\ 76+8=95-11 \\ 84=84 \end{gathered}[/tex]
Third equation:
[tex]\begin{gathered} 4(19)-11=2(19)+27 \\ 76-11=38+27 \\ 65=65 \end{gathered}[/tex]Then, as x=19 makes true all the equations. The value of x that makes ∆GTB= to ∆HAR is 19
