Analyze the geometric shapes in the image and determine their properties.

In parallelogram ABCD:

• Opposite sides are parallel and equal in length (AB || CD, BC || AD, AB = CD, BC = AD).
• Opposite angles are equal (∠A = ∠C, ∠B = ∠D).
• Adjacent angles are supplementary (∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, ∠D + ∠A = 180°).
• The sum of the angles is 360°.
• Diagonals bisect each other.

In triangle GRP:

• RO is perpendicular to GP (RO ⊥ GP).
• GO = OP (O is the midpoint of GP).

Since RO is an altitude and also a median, triangle GRP is an isosceles triangle with GR = RP. Also, RO is the angle bisector of ∠GRP.