Definition: Diagonals in a parallelogram are segments that connect opposite vertices.

Highlight: Theorem 43 proves that diagonals in a parallelogram bisect each other, a crucial property for many geometric proofs.

Example: In solving for diagonal lengths KM and LN, where KM = 48 and LN = 32, algebraic methods are used to find x = 16.

Vocabulary: Bisect means to divide into two equal parts.

Definition: A transversal is a line that intersects two or more other lines.

Example: When parallel lines create congruent segments PQ = QR = RS, the length of corresponding segments on other transversals will also be congruent.

Highlight: This theorem extends the properties of parallel lines beyond basic parallelogram concepts to more complex geometric relationships.

Vocabulary: Congruent segments are segments with equal lengths.

Definition: A parallelogram is a quadrilateral with opposite sides parallel.

Highlight: In parallelogram ABCD, AB = CD and BC = DA, demonstrating the congruence of opposite sides.

Example: When solving for angles in parallelogram PQRS, if one angle measures 64°, its consecutive angle can be found using the formula: mP + 64° = 180°, resulting in mP = 116°.

Vocabulary: Consecutive angles are adjacent angles in a geometric figure.