Question

On a piece of paper, use a protractor to construct right triangle DEF with DE=4 in. , m∠D=90° , and m∠E=45° .

Answer 1

Statement DF=4in. is true because: triangle DEF has a m∠D=90° so it is a right-angled triangle. But at the same time m∠E=45° so it is a isosceles triangle and a right-angled as well. 

Answer 2

Answer:   The answer is DF=4 inch.

Step-by-step explanation:  As shown in the attached figure, a right-angled triangle DEF is constructed using a protractor, where ∠D=90°, DE 4 inch and ∠E=45°.

So, according to the figure, EF is the hypotenuse of the triangle.

Now, in ΔDEF

∠D + ∠E + ∠F = 180°, which gives us

∠F = 180°-∠D - ∠E = 180° - 90° - 45° = 45°.

Hence, ∠E = ∠F. Thus, DE = DF, which implies that ΔDEF is an isosceles triangle also.

Thus, DF = 4 inch.