1. What is the plural of vertex?

Vertices. A triangle has three vertices (corners) .

2. What is the difference between an ALTITUDE and a MEDIAN in a triangle?

An ALTITUDE is a line from a vertex which meets the opposite side (or its extension) at right angles.
MEDIAN is a line from the vertex to the mid-point of the oppsoite side.

3. What is the difference between SIMILAR triangles and CONGRUENT triangles ?

SIMILAR triangles have the same shape but different size.

CONGRUENT triangles are the same shape and same size.

4. Is the longest side of a triangle always opposite the biggest angle?

Yes, and the SMALLEST angle is always opposite the SHORTEST side.