O R is a common side of two congruent quadrilaterals. In...

$\overline{O R}$ is a common side of two congruent quadrilaterals.
In your own words explain why each of the following statements must be true.
a. $O$ is the midpoint of $\overline{N M}$.
b. $\angle N O R \cong \angle M O R$
c. $\overline{R O} \perp \overline{N M}$
(GRAPH CANT COPY)

Key Concepts

Congruence

Congruence refers to the equality of shape and size between figures. In congruent figures, every corresponding pair of elements—whether they are sides, angles, or other segments—is equal. This concept supports the idea that if two figures are congruent, then the relationships and measurements in one figure are preserved in the other.

Reflection Symmetry

Reflection symmetry occurs when one half of a figure is the mirror image of the other across a specific line, often called the line of symmetry. In a scenario involving congruent figures sharing a common side, this symmetry implies that the parts of the figures on either side of the common line are corresponding images, ensuring that distances and angles mirror one another.

Midpoint

The midpoint of a segment is the point that divides the segment into two congruent parts. When a line of symmetry intersects a segment, it usually does so at its midpoint because the reflection maps one end of the segment to the other, guaranteeing equal partitioning.

Perpendicular Bisector

A perpendicular bisector is a line that both bisects a segment (divides it into two equal parts) and is perpendicular to it. In contexts where symmetry is involved, the line of reflection often serves as a perpendicular bisector, ensuring not only that the corresponding points on either side of the line are equidistant from the midpoint, but also that the angles formed are right angles, affirming the perpendicular nature.

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