$\text{ Let }L\text{ denote the set of all straight lines in a plane. Let a relation }R\text{ be defined by }\alpha R\beta \iff \alpha \perp \beta ,\alpha ,\beta \in L.\text{ Then, R is}$

$\text{ Here, }\alpha R\beta \iff \alpha \perp \beta \therefore \alpha \perp \beta \iff \beta \perp \alpha$

Hence, R is symmetric 

One line is not perpendicular to it self, so that R is not reflexive

Suppose (L,M), (M,N) are ordered pairs of R, it means L is perpendicular to M and M is perpendicular to N 

it does not implies that L is perpendicular to N, so that (M, N) does not belongs to R

so that R is not transitive