Solution:
Given : ∠ D E G= 51°, ∠GEF=39°
To prove: Δ D E F is a right triangle.
Proof:
A right angle triangle D E F.
∠ D E F =90°.
Point G is on segment D F, and segment E G is drawn.
Now, taking ∠DEG and ∠GEF into consideration,
∠DEG=51° and ∠GEF=39°→→(Given)
∠DEG + ∠GEF =
∠DEF=51° + 39°
∠DEF=90°,showing Triangle D E F is a right triangle.