Question

Find the area of an equilateral triangle having altitude of hcm. Prove that if a transversal intersects two parpllel lines the each pair of alternate interior angles are equal. If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are parallel. If a transversal intersects two parallel lines then each pair of consecutive interior angles are supplementary.

Answer 1

Area of an equilateral triangle having altitude of hcm:
Traingle ABC is an equilateral triangle with AD perpendicular
AD = hcm
by pythagoras theorm,
AB² = AD² + BD²
AB² =  h² + BC²/2
since AB = BC = AC
AB² = h² + AB²/2
AB = √2h
area of triangle ABC =√3/4AB² = √3/4 (√2h)²
√3/2h²cm2