ANSWERS
...The slope of FG and IH was 4/5. The slope of FI and GH was -5/4. Then I knew that ∠F, ∠G, ∠H, and ∠I were all right angles because perpendicular lines have opposite reciprocal slopes.
EXPLANATION
The slope of a line is given by,
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
For lines FG and IH, the slope is,
[tex]m_{FG}=m_{IH}=\frac{8}{10}=\frac{4}{5}[/tex]
Similarly, the slope of lines FI and GH is,
[tex]m_{FI}=m_{GH}=\frac{5}{-4}=-\frac{5}{4}[/tex]
Note that the slopes are opposite reciprocals, which makes each pair of lines perpendicular lines.
