Since m is a bisector of FH, we can draw the right triangle:
Now using the Pythagorean theorem, we can write:
[tex]\begin{gathered} EF^2=EG^2+FG^2 \\ EF^2=12^2+5^2 \end{gathered}[/tex]
And solve:
[tex]EF=\sqrt[]{12^2+5^2}=\sqrt[]{144+25}=\sqrt[]{169}=13[/tex]
EF = 13
Since m bisects FH,
[tex]FG=GH=5[/tex]
Finally, The triangle EGH is congruent with triangle EFG, by SAS. Then
[tex]EH=EF=13[/tex]
The whole answer is:
• EF = 13
,
• GH = 5
,
• EH = 13
