Prove that the line segments which join the midpoints of the oblique sides of a trapezium are parallel to the parallel sides.

In the figure below, $AB\parallel CD$, find $x$.

In the Fig., $AB\left|\right|CD$, find $x$.

In the figure,$P$ is the midpoint of $BC$ and $Q$ is the midpoint of $AP$. If $BQ$ (when produced) meets $AC$ at $R$, prove that $RA=\frac{1}{3}CA$.

Check whether the given pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form.

In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form.

In the figure below, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form.

In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form:

In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: