We want to solve for the missing sides of the right triangle.
The angles of the triangle are 45,45,90 degrees. therefore, this is an isosceles right triangle. Therefore, the Two shorter legs have the same length.
Therefore;
[tex]GI\cong HI[/tex]
Therefore,
[tex]GI=9[/tex]
To find HG, we usee pythagoras' theorem.
[tex]HG^2=GI^2+HI^2[/tex]
[tex]\begin{gathered} HG^2=9^2+9^2 \\ HG^2=2(9)^2 \end{gathered}[/tex]
Find square roots to get;
[tex]HG=9\sqrt[]{2}[/tex]
