Geometry Postulate, Theorem, and Corollary

Theorem 6.3	A diagonal of a parallelogram forms two congruent triangles.
Corollary 1	Opposite sides of a parallelogram are congruent.
Corollary 2	Opposite angles of a parallelogram are congruent.
Theorem 6.4	Consecutive angles of a parallelogram are supplementary.
Theorem 6.5	The diagonals of a parallelogram bisect each other.
Theorem 6.6	If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.7	If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6.8	If two sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Theorem 6.9	If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.10	Midsegment Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of the third side.
Theorem 6.11	If two fines are parallel, then all points of each line are equidistant from the other line.
Theorem 6.12	If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Corollary	If any number of parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Theorem 6.13	If a segment is parallel to one side of a triangle and contains the midpoint of a second side, then this segment bisects the third side.
Theorem 7.1	WAS for Congruent Quadrilaterals: Two quadrilaterals are congruent if any three sides and the included angles of one are congruent, respectively, to three sides and the included angles of the other.
Theorem 7.2	ASASA for Congruent Quadrilaterals: Two quadrilaterals are congruent if any three angles and the included sides of one are congruent, respectively, to three angles and the included sides of the other.
Theorem 7.3	The diagonals of a rhombus are perpendicular.
Theorem 7.4	The diagonals of a rectangle are congruent.
Theorem 7.5	Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 7.6	A parallelogram with one right angle is a rectangle.
Theorem 7.7	A parallelogram with two adjacent, congruent sides is a rhombus.
Theorem 7.8	A parallelogram with perpendicular diagonals is a rhombus.
Theorem 7.9	A parallelogram with congruent diagonals is a rectangle.

Note: The concepts in this collection may not be entirely accurate.
They are for reference only.

Geometry Postulate, Theorem, and Corollary

Part 5

Geometry Postulate, Theorem,
and Corollary