I need help with solving geometry proofs.

Question

Given: a/b = c/d

Prove: a/b = kc/kd

Answer 1

a/b=c/d

prove a/b=kc/kd

a/b=c/d    given

(c/d)(1)=c/d    multiplicative identity

k/k=1, k≠0    a number divided by itself is equal to 1 (or k(1/k)=1 which is multiplicative inverse)

(c/d)(k/k)    substitution; k/k=1 from above

(c/d)(k/k)=c/d    multiplicative identity (k/k=1)

(c/d)(k/k)=(ck/dk)   rule for multiplication of fractions ( if you consider that c/d is c times the multiplicative inverse of d, then you can prove the above  but that is a proof within itself and you'll have a proof in a proof so leave it as is)

if c/d=(c/d)(k/k) and (c/d)(k/k)=(ck/dk), then c/d=(ck/dk)     transitive property of equality

if a/b=c/d and c/d=(ck/dk), then a/b=ck/dk  transitive property of equality

a/b=kc/kd    commutative property of multiplication   (ck=kc and dk=kd   commutative property)