2. 3.1: Symmetry in Polygons Definition of polygon: a plane figure with three or more segments which intersect two other segments at the endpoints. No two segments with a common endpoint are collinear. The segments are called sides, and the endpoints are called vertices.

3. A common endpoint; a vertex Segment; side of polygon Two similar octagons

4. Types of Symmetry Reflectional symmetry: A figure has reflectional symmetry if and only if its reflected image across a line (line of symmetry) coincides exactly with the preimage.

5. Types of Symmetry (Continued) Rotational symmetry: A figure has rotational symmetry if and only if it has at least one rotation image, not counting rotation images of 0° or multiples of 360°. These two figures have rotational symmetry.

6. 3.2: Properties of Quadrilaterals Quadrilateral: Any four sided polygon. Certain quadrilaterals have specific properties and these are called special quadrilaterals. They include trapezoids, parallelograms, rhombuses, rectangles and squares.

7. Trapezoids A trapezoid is a quadrilateral with one and only one pair of parallel sides These two sides are parallel. They are the only set.

8. Parallelograms A parallelogram is a quadrilateral with two pairs of parallel sides. Conjectures: Opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and the diagonals bisect each other.

9. Rhombuses Rhombus: A quadrilateral with four congruent sides Conjectures: All rhombuses are parallelograms, therefore all conjectures for the parallelogram holds true for the rhombus, diagonals are perpendicular bisectors.

10. Rectangles Rectangle: A quadrilateral with four right angles Conjecture: A rectangle is a parallelogram, therefore all conjectures for parallelogram hold true for rectangles, diagonals are congruent.

11. Squares Square: A quadrilateral with four congruent sides and four right angles Conjectures: A square is a rectangle, parallelogram and rhombus. All conjectures for those figures hold true for the square, Diagonals bisect each other, are congruent and are perpendicular bisectors.

12. 3.3: Parallel lines and Transversals Parallel lines: two coplanar lines that do not meet no matter how far they might be extended Transversal: A line, ray or segment that intersects tow or more coplanar lines, rays or segments each at a different point.

13. The Beatles- Mathematicians in Disguise? These lines on the road are parallel! The Beatle are clearly forming a transversal on Abbey Road!

14. Postulates/ Theorems Corresponding Angles Postulate: If two lines cut by a transversal are parallel, then corresponding angles are congruent. Alternate Interior Angles Theorem: If two lines cut by a transversal are parallel, then alternate interior angles are congruent Alternate Exterior Angles theorem: If two lines cut by a transversal are parallel, then alternate exterior angles are congruent

15. Postulates/ Theorems (Continued) Same Side Interior Angles Theorem: If two lines cut by a transversal are parallel, then same side interior angles are supplementary.

16. Corresponding angles: 1+5, 2+6, 3+7, 4+8 Alternate interior angles: 3+6, 4+5 Alternate exterior angles: 1+8, 2+7 Same side interior angles: 3+5, 4+6 Same side exterior angles: 1+7, 2+8

17. 3.4: Proving That Lines Are Parallel You know from 3.3 how to determine angle measures if you know the lines are parallel, but is the converse is also true? It is.

18. Theorems Converse of the Same-Side Interior Angles Theorem: If two lines are cut by a transversal in such a way that same side interior angles are supplementary, then the two lines are parallel. Converse of the Alternate Interior Angles theorem: if two lines are cut by a transversal in such a way that alternate interior angles are congruent, then the two lines are parallel.

19. Theorems Converse of the Alternate Exterior Angles Theorem: If two lines are cut by a transversal in such a way that alternate exterior angles are congruent, then the two lines are parallel. Theorem: If two coplanar lines are perpendicular to the same line then the two lines are parallel to each other. Theorem: If two coplanar lines are parallel to the same line, then the two lines are parallel to each other.

20. Review for Exam The website below offers important vocabulary terms and postulates which will help you review for the exam. Click Me!

21. Bibliography "Parallels and Polygons." 1. Web. 8 Dec 2009.. Schultz, Hollowell, Ellis, Kennedy, Engelbrecht, Rutowski,. Geometry. Austin: Holt, Rinehart and Winston, 2001. 138-69. Print.