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Transcript
Aim: How do we think like a mathematician? Do Now: July 16, 2012 S Things to look out for: S Vertical Angles S S S S S S (LinesAnglesPlanesTriangles Slide 27) Alternate Exterior/Interior Angles Corresponding Angles Conditional Statement Transitive Property Similar Triangles Mid-Segment Symbols S || Parallel S ≅ Congruent S ~ Similar Think Like A Mathematician! Congruent Angles and Segments S When angles are congruent, we mark with an arc. S Use multiple marks to show different relationships. S ∠ A ≅ ∠ D, ∠ B ≅ ∠ F S AB ≅ DF, AC ≅ DE S What other relationship do you see? Think Like A Mathematician! Parallel Lines S Parallel lines are marked with arrows. S a || b Think Like A Mathematician! S Many theorems and postulates are in the form of Conditional statements (If-Then statements) S Ex: Transitive Property – IF a = b and b = c, THEN a = c S There is no room for guesswork or assumptions in logic. S Use only given information to come to logical conclusions. S Every statement must have a reason. Think Like A Mathematician! S In mathematics we cannot make a statement unless we can prove it. S All of the theorems and rules of geometry can be proven. S Let’s prove that Vertical Angles are congruent. S On the next slide, we will do a basic statement-reason proof. S As part of our proof, we will be using the Transitive Property Think Like A Mathematician! Statement Reason S AC intersects BD at E S Given S m∠AEB = m∠BEC – 180 S Supplementary Angles add up to 180 S m∠BEC – 180 = ∠DEC S Supplementary Angles add up to 180 S ∠AEB ≅ ∠DEC S Transitive Property Think Like A Mathematician! S Read through the following PowerPoint presentations found at http://www.ptechnyc.org/page/114 S LinesAnglesPlanesTriangles S PolygonProperties S Midpoint PowerPoint S Take note of all the vocabulary words and their definitions. S In groups of 3 or 4, Complete the assignment “Transversals and Triangle sum proof.doc” S Place completed assignment in your folder. Khan Academy Week 1 S S S S S S S S S Recognizing rays lines and line segments Parallel lines 1 Points lines and planes Combining like terms Combining like terms with distribution Alternate exterior angles Same side exterior angles Alternate exterior angles 2 Same side exterior angles 2
