Given: C(0,0), A(d,e), T(c + d, e) and S(c,0). Prove that CATS is a parallelogram.

Question

Given: C(0,0), A(d,e), T(c + d, e) and S(c,0). Prove that CATS is a parallelogram.

Answer 1

Compute the slopes of each side:

CA: (e-0)/(d-0) = e/d

AT: (e-e)/(c+d-d) = 0

TS: (e-0)/(c+d-c) = e/d

SC: (0-0)/(c-0) = 0

CA and TS have equal slopes so they are parallel

AT and SC have equal slopes so they are parallel

CA and TS are opposite sides of the quadrilateral

AT and SC are opposite sides of the quadrilateral

If opposite sides of a quadrilateral are parallel then it is a parallelogram