A right-angled triangle DEF is constructed with DE = 5 cm, ∠F = 90°, and DF = 4 cm. Choose the correct statement from the following.
Given: ∠F = 90°
So, the hypotenuse is the side opposite to ∠F, which is DE.
And the other two sides are DF and EF.
Using Pythagoras theorem,
DE2=DF2+EF2
⟹ 52=42+EF2
⟹ EF2=52−42=25−16
⟹ EF2=9=32
Hence, EF = 3 cm
By the angle sum property, ∠D + ∠E + ∠F = 180°
⟹ ∠D + ∠E = 180° - ∠F = 180° - 90° = 90°
Hence, ∠E + ∠D = 170° is false.
And, the hypotenuse of a right-angled triangle is the side opposite to the right angle.Therefore, the hypotenuse of △DEF, which is right-angled at F, is DE not DF.