Construct triangleEFG, where angleG=90, EF=10cm and angleE=45. Compare FG and EG .

Steps for constructing a triangle:
STEP I: Take any point G and draw a line passing through G.
STEP II: Draw a line perpendicular to the line passing through G and intersecting at a point G.
STEP III: Take any point E on this perpendicular line.
STEP IV: Taking the point E, draw a line EF = 10 cm such that it intersects the line passing through G and $\angle \mathrm{GEF} = 45°$
Therefore, we get the required triangle EFG
Now in triangle EFG, we have
$\angle G = 90° \mathrm{and} \angle E = 45°$
So, $\angle F = 180°-\left(\angle G+\angle E\right) = 180°-\left(90°+45°\right) = 45°$
Therefore, $\angle E = \angle F = 45°$.
Now we know that equal angles have equal sides.
So, FG = EG