Question

Which geometric principle is used to justify the construction below?

(a) A line perpendicular to one of two parallel lines is perpendicular to the other

(b) Two lines are perpendicular if they intersect to form congruent adjacent angles

(c) When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel

(d) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel

I had been asked this question by my college professor while I was bunking the class.

I want to ask this question from Geometrical Construction topic in chapter Lettering Practice, Scales & Curves of Civil Engineering Drawing

Answer 1

Right option is (d) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel

The best explanation: ∠A, ∠F, ∠G, ∠D are exterior angles. ∠B, ∠E, ∠H, ∠C are interior angles. ∠B and ∠E, ∠H and ∠C are consecutive interior angles. ∠A and ∠G, ∠F and ∠D are alternate exterior angles. ∠E and ∠C, ∠H and ∠B are alternate interior angles. ∠A and ∠E, ∠C and ∠G ∠D and ∠H, ∠F and ∠B are corresponding angles.