To convert the polar equation \( r = \frac{2}{1 + \cos \theta} \) into its rectangular form, we start by eliminating the fraction. We do this by multiplying both sides by the denominator \( 1 + \cos \theta \), resulting in:

\( r(1 + \cos \theta) = 2 \)

This simplifies to:

\( r + r \cos \theta = 2 \)

Next, we recognize that \( r \cos \theta \) can be replaced with \( x \) (since \( r \cos \theta = x \)), and we also need to express \( r \) in terms of \( x \) and \( y \). We know that:

\( r = \sqrt{x^2 + y^2} \)

Substituting these into the equation gives us:

\( \sqrt{x^2 + y^2} + x = 2 \)

To eliminate the square root, we first isolate it:

\( \sqrt{x^2 + y^2} = 2 - x \)

Next, we square both sides to remove the square root:

\( x^2 + y^2 = (2 - x)^2 \)

Expanding the right side results in:

\( x^2 + y^2 = 4 - 4x + x^2 \)

We can simplify this by canceling \( x^2 \) from both sides:

\( y^2 = 4 - 4x \)

This equation can be rearranged to:

\( y^2 = -4x + 4 \)

Recognizing the form of this equation, we see that it represents a horizontal parabola. The standard form of a horizontal parabola is given by \( (y - k)^2 = 4p(x - h) \), where \( (h, k) \) is the vertex. In this case, the vertex is at \( (1, 0) \) and it opens to the left.

In summary, the polar equation \( r = \frac{2}{1 + \cos \theta} \) converts to the rectangular form \( y^2 = 4 - 4x \), which describes a horizontal parabola.