# Geometry Chapter 8

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1. Diagonal of a Polygon
A segment that joins two nonconsecutive vertices of a polygon.
2. Interior Angles of a Triangle
The angles on the inside of a triangle.
3. Exterior Angles of a Triangle
The angles on the outside of the triangle.
4. Theorem 8.1: POLYGON INTERIOR ANGLES THEOREM
• The sum of the measures of the interior angles:
• ( n - 2 ) * 180 n = number of sides in a triangle
5. Corollary To Theorem 8.1: INTERIOR ANGLES OF A QUADRILATERAL
The sum of the measures of the interior angles of a quadrilateral is ALWAYS 360
6. Theorem 8.2: POLYGON EXTERIOR ANGLES THEOREM
The sum of the measures of the exterior angles of a convex polygon is ALWAYS 360
7. Parallelogram
A quadrilateral with both pairs of opposite sides parallel.
8. Theorem 8.3:
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
9. Theorem 8.4:
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
10. Theorem 8.5:
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
11. Theorem 8.6:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
12. Theorem 8.7:
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
13. Theorem 8.8:
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
14. Theorem 8.9:
If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
15. Theorem 8.10:
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
16. Rhombus
A parallelogram with four congruent sides.
17. Rectangle
A parallelogram with four right angles.
18. Square
A parallelogram with four congruent sides and four right angles.
19. Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
20. Theorem 8.11:
A parallelogram is a rhombus if only if its diagonals are perpendicular.
21. Theorem 8.12:
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
22. Theorem 8.13:
A parallelogram is a rectangle if and only if its diagonals are congruant.
23. Trapezoid
A quadrilateral with exactly one pair of parallel sides.
24. Bases of a Trapezoid
The parallel sides of a trapezoid.
25. Base Angles of a Trapezoid
Trapezoid has 2 pairs of base angles; each pair surrouds a base.
26. Legs of a Trapezoid
The non-parallel sides of a trapezoid.
27. Isosceles Trapezoid
Trapezoid with congruent legs.
28. Midsegment of a Trapezoid
Segments that connects the midpoints of the legs of a trapezoid.
29. Kite
Quadrilateral with 2 pairs of consecutive congruent sides ( opposite sides are not congruant )
30. Theorem 8.14:
If a trapezoid is isoceles, then each pair of base angles is congruant.
31. Theorem 8.15:
If a trapezoid has a pair of congruent base angles, then its an isoceles trapezoid.
32. Theorem 8.16:
A trapezoid is isosceles if and only if its diagonals are congruent.
33. Theorem 8.17: MIDSEGMENT THEOREM FOR TRAPEZOIDS
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
34. Theorem 8.18:
If a quadrilateral is a kite, then its diagonals are perpendicular.
35. Theorem 8.19:
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
 Author: john708 ID: 133917 Card Set: Geometry Chapter 8 Updated: 2012-02-09 04:40:23 Tags: Geometry Chapter Folders: Description: Geometry Chapter 8 Show Answers: