1.  Aim: How do we think like a mathematician? Do Now: July 16, 2012

2. Things to look out for:  Vertical Angles (LinesAnglesPlanesTriangles Slide 27)  Alternate Exterior/Interior Angles  Corresponding Angles  Conditional Statement  Transitive Property  Similar Triangles  Mid-Segment Symbols  || Parallel  ≅ Congruent  ~ Similar

3. Think Like A Mathematician! Congruent Angles and Segments  When angles are congruent, we mark with an arc.  Use multiple marks to show different relationships.  ∠ A ≅ ∠ D, ∠ B ≅ ∠ F  AB ≅ DF, AC ≅ DE  What other relationship do you see?

4. Think Like A Mathematician! Parallel Lines  Parallel lines are marked with arrows.  a || b

5. Think Like A Mathematician!  Many theorems and postulates are in the form of Conditional statements (If-Then statements)  Ex: Transitive Property – IF a = b and b = c, THEN a = c  There is no room for guesswork or assumptions in logic.  Use only given information to come to logical conclusions.  Every statement must have a reason.

6. Think Like A Mathematician!  In mathematics we cannot make a statement unless we can prove it.  All of the theorems and rules of geometry can be proven.  Let’s prove that Vertical Angles are congruent.  On the next slide, we will do a basic statement-reason proof.  As part of our proof, we will be using the Transitive Property

7. Think Like A Mathematician! Statement  AC intersects BD at E  m ∠ AEB = m ∠ BEC – 180  m ∠ BEC – 180 = ∠ DEC  ∠ AEB ≅ ∠ DEC Reason  Given  Supplementary Angles add up to 180  Transitive Property

8. Think Like A Mathematician!  Read through the following PowerPoint presentations found at http://www.ptechnyc.org/page/114 http://www.ptechnyc.org/page/114  LinesAnglesPlanesTriangles  PolygonProperties  Midpoint PowerPoint  Take note of all the vocabulary words and their definitions.  In groups of 3 or 4, Complete the assignment “Transversals and Triangle sum proof.doc”  Place completed assignment in your folder.

9. Khan Academy Week 1  Recognizing rays lines and line segments Recognizing rays lines and line segments  Parallel lines 1 Parallel lines 1  Points lines and planes Points lines and planes  Combining like terms Combining like terms  Combining like terms with distribution Combining like terms with distribution  Alternate exterior angles Alternate exterior angles  Same side exterior angles Same side exterior angles  Alternate exterior angles 2 Alternate exterior angles 2  Same side exterior angles 2 Same side exterior angles 2