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

Steps for constructing a triangle:

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 $\angle \mathrm{GEF}=45\xb0$

Therefore, we get the required triangle EFG

Now in triangle EFG, we have

$\angle G=90\xb0\mathrm{and}\angle E=45\xb0$

So, $\angle F=180\xb0-\left(\angle G+\angle E\right)=180\xb0-\left(90\xb0+45\xb0\right)=45\xb0$

Therefore, $\angle E=\angle F=45\xb0$.

Now we know that equal angles have equal sides.

So, FG = EG

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