$\inline&space;xOy$ The Euclidean plane $\inline&space;&space;Ox$ The $\inline&space;x$-axis of the Euclidean plane $\inline&space;Oy$ The $\inline&space;y$-axis of the Euclidean plane $\inline&space;A,\,&space;B,\,&space;C,\,&space;\ldots$ Points in the Euclidean plane with certain coordinates $\inline&space;A(x_A,&space;y_A)$, $\inline&space;B(x_B,&space;y_B)$, $\inline&space;C(x_C,&space;y_C)$, etc. $\inline&space;&space;AB$ The line that passes through points $\inline&space;A$ and $\inline&space;B$ $\inline&space;&space;A&space;-&space;B&space;-&space;C}$ This says that the points $\inline&space;A$, $\inline&space;B$ and $\inline&space;C$ are collinear, i.e. there exists a unique line which passes through all of them. $\inline&space;&space;[AB]$ The segment with endpoints $\inline&space;A$ and $\inline&space;B$ $\inline&space;&space;|AB|$ The length of the segment with endpoints $\inline&space;A$ and $\inline&space;B$ $\inline&space;&space;l_1&space;\parallel&space;l_2$ This says that the lines $\inline&space;l_1$ and $\inline&space;l_2$ are parallel, i.e. they do not have any points in common. $\inline&space;&space;l_1&space;\perp&space;l_2$ This says that the lines $\inline&space;l_1$ and $\inline&space;l_2$ are perpendicular, i.e. they form a right angle at their point of intersection. $\inline&space;&space;d(A,&space;B)$ The distance between the points $\inline&space;A$ and $\inline&space;B$ $\inline&space;&space;d(A,&space;l)$ The distance between the point $\inline&space;A$ and the line $\inline&space;l$ $\inline&space;&space;\angle&space;O,&space;\angle&space;AOB$ The angle with vertex $\inline&space;O$ and rays $\inline&space;OA$, $\inline&space;OB$ $\inline&space;&space;\triangle&space;ABC$ The triangle with vertices $\inline&space;A$, $\inline&space;B$ and $\inline&space;C$ $\inline&space;&space;\triangle&space;ABC&space;\equiv&space;\triangle&space;PQR$ This says that the triangles $\inline&space;\triangle&space;ABC$ and $\inline&space;\triangle&space;PQR$ are congruent, which means that $|AB|&space;=&space;|PQ|&space;\qquad&space;|AC|&space;=&space;|PR|&space;\qquad&space;|BC|&space;=&space;|QR|.$ $\inline&space;&space;\triangle&space;ABC&space;\sim&space;\triangle&space;PQR$ This says that the triangles $\inline&space;\triangle&space;ABC$ and $\inline&space;\triangle&space;PQR$ are similar, which basically means $\frac{|AB|}{|PQ|}&space;=&space;\frac{|AC|}{|PR|}&space;=&space;\frac{|BC|}{|QR|}.$ $\inline&space;&space;[ABCD]$ The quadrilateral with vertices $\inline&space;A$, $\inline&space;B$, $\inline&space;C$ and $\inline&space;D$ $\inline&space;&space;\mathcal{A}_{\triangle&space;ABC}$ The area of the triangle $\inline&space;\triangle&space;ABC$ $\inline&space;&space;\mathcal{A}_{[ABCD]}$ The area of the quadrilateral $\inline&space;[ABCD]$ $\inline&space;&space;\mathcal{C}(O,&space;R)$ The circle with center at the point $\inline&space;O$ and radius equal to $\inline&space;R$