Identify the types of quadrilaterals based on their properties.

Here are the answers to the questions:

1. A quadrilateral whose opposite sides are parallel is called a $\boxed{\textbf{parallelogram}}$. Let the quadrilateral be $ABCD$. Given: $AB \parallel CD$ and $AD \parallel BC$. Therefore, $ABCD$ is a parallelogram.

2. A quadrilateral with all sides equal and each angle is $90^\circ$ is a $\boxed{\textbf{square}}$. Let the quadrilateral be $PQRS$. Given: $PQ = QR = RS = SP$ and $\angle P = \angle Q = \angle R = \angle S = 90^\circ$. Therefore, $PQRS$ is a square.