Test 1 Flashcards
Right Triangle
Three sided figure with one right angle
Acute Triangle
Three sided figure with all angles less than a right angle
Obtuse Triangle
Three sided figure with one angle larger than a right angle
Isosceles Triangle
Three sided figure with at least two equal sides
Equilateral Triangle
Three sided figure with three equal sides
Equiangular Triangle
Three Sided figure with three equal angles
Scalene Triangle
Three sided figure with no two sides equal
Square
Four sided figure with four congruent sides, and four right angles
Rectangle
Four sided figure with four right angles
Rhombus
Four sided figure with four congruent sides
Parallelogram
Four sided figure with two sets of parallel sides
Kite
Four sided figure with two sets of congruent adjacent sides
Trapezoid
Four sided figure with exactly one set of parallel sides
Definition
A description of a shape or situation that is accepted as true by an authoritative body of people
Pi
circumference/diameter
If 2 things are equal to a third
then those 2 things are equal
If equals are added to equals
then the sums are equal
If equals are subtracted from equals
then the differences are equal
If 2 things coincide with one another
then they are equal
If there are 2 points (Postulate 1)
then there is a line segment between those 2 points
If there is a line segment
then it can be extended
If there are 2 points (Postulate 3)
then there is a circle centered at one point going through the other point
If there are 2 right angles
then they are congruent
Axiom 5
Whole is greater than any of its parts
Construct an equilateral triangle
Construct a kite
Construct a rhombus
Construct an isosceles triangle
Construct a rectangle
Construct a square
Duplicate an angle
Axiom
mathematical statement accepted as true which CANNOT be proven
Postulate
geometrical statement accepted as true which CANNOT be proven
Property
mathematical statement about a shape or relationship that can be or has been proved to be true … and cannot be part or easily derivable from the definition.
Rotational Symmetry
2 requirements
Give an example
when an object is rotated on its own axis and looks the same after a rotation
center point and angle
a circle
Reflective Symmetry
2 requirements
Give an example
when a figure has a line of symmetry indicating that both halves look exactly the same
line of reflection
the capital letter A
Concrete Teaching/Learning
students manipulate 3D objects
Axiomatic Geometry
theorems are proved using definitions, axioms, postulates, and previously proven theorems by means of accepted rules of logic
Differences between definition and property
difference: the definition has been accepted as true, whereas, property must be proven to be true
similarity: both statements are true
chord
line segment who’s points are on a circle
List 4 aspects of geometry in the world
sports, the game of pool, music, nature, and architecture
Van Hiele Level 0
Recognition
students don’t know shapes and definitions, cannot distinguish between relevant and irrelevant attributes
kids basically recognize for what they know it to be
Van Hiele Level 1
Analysis
student focuses analytically on components parts and their attributes
they begin to explore properties, might not believe they belong to several classes
Van Hiele Level 2
Relationships
student begins to understand relationships among figures
become better communicators and begin to think abstractly
Van Hiele Level 3
Deduction
student can study geometry as a formal mathematical system and write formal proofs of theorems
abstract thinking (work is done mentally)
