When two lines intersect, the angles opposite each other (vertical angles) are always equal. Therefore, the correct statement is that vertical angles are always equal.

All quadrilaterals are indeed polygons, as they are defined as shapes with four sides, which fits the definition of a polygon.

The slope between any two pairs of these points is the same (1), indicating they are collinear.

Parallel lines have the same slope, hence their slopes are equal.

A polygon with all sides and angles equal is known as a regular polygon.

A line that touches a circle at exactly one point is called a tangent.

A tangent is defined as a line that touches a circle at exactly one point.

A chord is defined as a line segment whose endpoints lie on the circle.

A regular polygon is defined as a polygon where all sides and angles are equal.

A trapezoid is defined as a polygon that has exactly one pair of parallel sides.

For a given base, an equilateral triangle has the maximum area compared to other types of triangles.

Using the formula for the area of a triangle, the triangle with sides 7, 24, 25 has the largest area due to its larger base and height.

A rhombus has all sides equal, but the angles are not necessarily equal.

In a trapezium, the diagonals are not equal and do not bisect each other.

In a rhombus, the diagonals are perpendicular bisectors of each other.

A kite has two pairs of adjacent sides that are equal.