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

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