Chapter 1 Using Geogebra. Doing Mathematics Geogebra  Dynamic  Easier to see what happens to geometric objects Make observations Formulate conjectures.

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Presentation transcript:

Chapter 1 Using Geogebra

Doing Mathematics Geogebra  Dynamic  Easier to see what happens to geometric objects Make observations Formulate conjectures  If … [hypothesis] … then … [conclusion]…

Conjectures Hypothesis  Assumptions Conclusion  What happens when assumptions hold Often expressed using  If … then …

Conjectures Ask yourself  What is happening  Why is it happening  What properties of figures made it happen

Geogebra Tips Straight edge tools

Geogebra Tips Polygon tools

Geogebra Tips Circle tools

Geogebra Tips Changing object property – color

Geogebra Tips Using arrow tool  Drag a point, view results

Geogebra Tips The Point tool  Use to establish an intersection

Observing, Conjecturing Inductive reasoning  Examine examples  Discover patterns Deductive reasoning  Justify the conjecture  Find explanation why conjecture holds  Proof

Language of Geometry Formal definitions  Precision necessary  Math definitions are prescriptive Definition different from properties  Example: define rectangle  Construct figure only with definition

Polygons Closed figure  In the plane  Formed by set of line segments  Each segment shares each endpoint with exactly 1 other line segment Poly -  many - gons  angles

Quadrilateral Joining midpoints of arbitrary quadrilateral?

Quadrilateral Self intersecting polygon

Quadrilateral Concave polygon

Viviani’s Theorem What was the sum of l + m + n ?  What if P was outside the triangle?  What if the triangle was not equilateral?  What if it is a square? P

Family of Quadrilaterals Identify the categories

Angles Inscribed in Circles What relationships did you find?

Rules of Logic Statements … open? closed? true? false?  All cars are blue.  The car is red.  Yesterday was Sunday.  Rectangles have four interior angles.  Construct the perpendicular bisector.

Rules of Logic Use logical operators  and, or Evaluate truth of logical combinations  P and Q

Rules of Logic Combining with or  P or Q

Rules of Logic Negating a statement  not P

Chapter 1 Using Geogebra

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