1. Y. Davis Geometry Notes
Chapter 6

2. Diagonal
A segment that connects 2 non-consecutive vertices of a polygon

3. Theorem 6.1 Polygon Interior Angles Sum
The sum of the interior angles of any convex n-gon is

4. Theorem 6.2 Polygon Exterior Angles Sum
The sum of the exterior angle measures a convex polygon, one angle at each vertex, is 360 degrees.

5. Parallelogram
A quadrilateral with both pair of opposite sides parallel.

6. Properties of parallelograms
Theorem 6.3—If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6.4—If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Theorem 6.5—If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Theorem 6.6—If a parallelogram has 1 right angle, then it has 4 right angles.

7. Diagonals of Parallelogram
Theorem 6.7—If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6.8—If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into 2 congruent triangles.

8. Conditions for Parallelograms
Theorem 6.9—If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
Theorem 6.10—If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.
Theorem 6.11—If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Theorem 6.12—If one pair of opposite sides of a quadrilateral is both parallel and congruent, then it is a parallelogram.

9. Rectangle A parallelogram with 4 right angles.
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles are supplementary
Diagonals bisect each other.

10. Theorem 6.13 diagonals of a rectangle
If a parallelogram is a rectangle, then its diagonals are congruent.

11. Theorem 6.14 Prove parallelograms are rectangles
If the diagonals of a parallelogram are congruent, then it is a rectangle.

12. Rhombus A parallelogram with 4 congruent sides
Opposite sides congruent and parallel
Opposite angles congruent.
Consecutive sides supplementary
Diagonals bisect each other.

13. Diagonals of a Rhombus
Theorem 6.15—If a parallelogram is a rhombus, then its diagonals are perpendicular.
Theorem 6.16—If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

14. Square A parallelogram with 4 congruent sides and 4 right angles.
Opposite sides parallel and congruent.
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other.
Diagonals congruent
Diagonals perpendicular
Diagonals bisect each pair of opposite angles.

15. Conditions for Rhombi
Theorem 6.17—If the diagonals of a parallelogram are perpendicular, then it is a rhombus.
Theorem 6.18—If a diagonal of a parallelogram bisect a pair of opposite angles, then it is a rhombus.
Theorem 6.19—If one pair of consecutive sides of a parallelogram are congruent, then it is a rhombus

16. Conditions for Squares
Theorem 6.20—If a parallelogram is both a rectangle and rhombus, then it is a square.

17. Trapezoids
A quadrilateral with exactly one pair of opposite sides parallel.
Bases—parallel sides
Legs—non-parallel sides
2 pair of Base Angles–each pair includes a base.

18. Isosceles Trapezoid A trapezoid with congruent legs.
Theorem 6.21—If a trapezoid is isosceles, then each pair of base angels are congruent.
Theorem 6.22—If a trapezoid has one pair of congruent base angles, then it is isosceles.
Theorem 6.23—A trapezoid is isosceles if and only if its diagonals are congruent.

19. Midsegment of aTrapezoid
The segment that connects the midpoints of the legs of a trapezoid.

20. Theorem 6.24 Trapezoid Midsegment Theorem
The Midsegment of a trapezoid is parallel to the 2 bases and ½ the sum of the bases.

21. Kite
A quadrilateral with exactly 2 pairs of consecutive sides congruent, but no opposite sides congruent.

22. Kites
Theorem 6.25—If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 6.26—If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.