Inductive and Deductive Reasoning in geometry:
Inductive Reasoning: The process of observing data, recognizing patterns, and making generalizations about those patterns.
Deductive Reasoning: The process of showing that certain statements follow logically form agreed-upon assumptions and proven facts.
(Definitions found in Discovering Geometry An Investigative Approach by Michael Serra)
Recognizing patterns and modeling them with equations:
X
|
1
|
2
|
3
|
4
|
5
|
6
|
…
|
X
|
f(X)
|
-8
|
-1
|
6
|
13
|
20
|
27
|
…
|
f(x)=7x-15
|
-1=7(2)+n f(x)=7x-15
-14
-15=n
Special Angle Relationship
Points of Concurrency:
Incenter: Intersecting point a triangles angle bisectors.
Circumcenter: Intersecting point of the triangle perpendicular bisector.
Orthocenter: Intersecting point of the triangle altitudes.
Centroid: Intersecting point of the triangle medians.
Constuction with compass and straight edge:
Discovering and Proving Triangle Properties:
If you have two triangles with the following congruences they are conguent:
Side-Side-Side, Side-Angle-Side, Side-Angle-Angle, Angle-Side-Angle.
If you have two triangles with the following congruences they are not congruent:
Angle-Angle-Angle, Angle-Side-Side.
Topic I enjoyed!!!! This rule really made alot of sense to me and I really loved how simple and logical this topic was. On the chapter five test you can see my understanding of this consept!
Triangle Sum Conjecture: The sum of the measures of the angle in every triangle is 180 degrees.
Isosceles Triangle Sum Conjecture: Base angles are congruent.
The Triangle Inequality Conjecture: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Side-Angle Inequality Conjecture: The longer side is opposite to the largest angle, the smallest side is opposite to the smallest angle.
Discovering and Proving Polygon Properties:
Polygon Sum Conjecture: The sum for the interior angles of the polygon adds up to 180(n-2) or 180n-360. n=number of sides of polygon.
Equaianglular Polygon Conjecture; Each interior angle of an equiangular "n"-gon measures are all equal.
Exterior Angles of a Polygon: In any polygon the sum of a set exterior angles add up to 360 degrees.
"The mathematician does not study pure mathematics because it is useful; he studies it because it is beautiful."
-J.H. Poincare (1854-1912)
This quote only rings true to some math for me. There is some math that I love to do and I find satesfying. But other math is just plain boring or just plain frustrating. Truethfully I find most of the Geometry boring, repetitive, and something I will forget the second I'm no longer using these "conjectures". At the moment MATH IS NOT BEAUIFUL!!!!!!!!!
Compbook Exstravaganza!!!
I find this section of the my compbook very pretty:
Circumcenter: Intersecting point of the triangle perpendicular bisector.
Orthocenter: Intersecting point of the triangle altitudes.
Centroid: Intersecting point of the triangle medians.
Constuction with compass and straight edge:
If you have two triangles with the following congruences they are conguent:
Side-Side-Side, Side-Angle-Side, Side-Angle-Angle, Angle-Side-Angle.
If you have two triangles with the following congruences they are not congruent:
Angle-Angle-Angle, Angle-Side-Side.
Topic I enjoyed!!!! This rule really made alot of sense to me and I really loved how simple and logical this topic was. On the chapter five test you can see my understanding of this consept!
Triangle Sum Conjecture: The sum of the measures of the angle in every triangle is 180 degrees.
Isosceles Triangle Sum Conjecture: Base angles are congruent.
The Triangle Inequality Conjecture: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Side-Angle Inequality Conjecture: The longer side is opposite to the largest angle, the smallest side is opposite to the smallest angle.
Discovering and Proving Polygon Properties:
Polygon Sum Conjecture: The sum for the interior angles of the polygon adds up to 180(n-2) or 180n-360. n=number of sides of polygon.
Equaianglular Polygon Conjecture; Each interior angle of an equiangular "n"-gon measures are all equal.
Exterior Angles of a Polygon: In any polygon the sum of a set exterior angles add up to 360 degrees.
"The mathematician does not study pure mathematics because it is useful; he studies it because it is beautiful."
-J.H. Poincare (1854-1912)
This quote only rings true to some math for me. There is some math that I love to do and I find satesfying. But other math is just plain boring or just plain frustrating. Truethfully I find most of the Geometry boring, repetitive, and something I will forget the second I'm no longer using these "conjectures". At the moment MATH IS NOT BEAUIFUL!!!!!!!!!
Compbook Exstravaganza!!!
I find this section of the my compbook very pretty:
