Suggested
Enrichment Program Using Cinderella (DGS)
© 20072008 Mohamed ElDemerdash
The Suggested Enrichment Program Outcomes
Handout1
Launching and Exploring Cinderella
Handout 2
Basic Commands and Constructions (Modes) of Cinderella
Handout 3
Enrichment Program Activities
Activity 1: Dragging and Measuring Facilities of Cinderella
Handout 4
Warm up Constructions

The Sum of Measures of the Interior Angles of a Triangle

The Sum of the Accumulative Angles at a Point
The Activity Problem
Follow up Problems

Proposed Problem 1: Four Triangles Equal in Perimeter

Proposed Problem 2: Area Relationship

Proposed Problem 3: Four Congruent Triangles

Proposed Problem 4: Five Similar Triangles

Proposed Problem 5: The Type of the Four Obtained Triangles
Activity 2: Automatic Proving Facilities of Cinderella
Handout 5
Warm up Questions
The Activity Problem
Follow up Conjectures

Conjecture 1: The Relationship between the Line of Centers and the Common Chord

Conjecture 2: Quadrilateral Kite

Conjecture 3: Congruent Triangle

Conjecture 4: The Line of Centers as an Angular Bisector

Conjecture 5: Parallelism Relationship

Conjecture 6: Similar Triangles

Conjecture 7: Rectangle

Conjecture 8: Area Relationship 1

Conjecture 9: Area Relationship 2

Conjecture 10: Area Relationship 3
Activity 3: Developing Macroconstructions
Handout 6
Macroconstructions

Perpendicular Bisector

Circumcenter Point of a Triangle

Incenter Point of a Triangle

Orthocenter Point of a Triangle

Center of Mass or Centroid Point of a Triangle

Euler Line of a Triangle

Euler Ratio of a Triangle

Euler Circle or Nine Point Circle
Activity 4: Animating and Tracing Loci Facilities of Cinderella
Handout 7
Warm up Constructions
The Activity Problem
Other Geometric Loci Related to triangle

The Locus of the Intersection Point of Medians of a Triangle

The Locus of the Intersection Point of Angular Bisectors of the Interior Angles of a Triangle

The Locus of the Intersection Point of Perpendicular Bisectors of the Sides of a Triangle
Furthermore, the situation can be elaborated to discover and generate other loci by considering the intersection point of two different lines in the triangle such as the intersection point of a height and a median, the intersection point of a median and a perpendicular bisector, etc.
The below table is used to organize the situations design with a notice that the line in the header of the table is the line, which moves through the movable vertex (the vertex C).
Height (H)  Median (M)  Angular Bisector (A. B.)  
Height (H)  Heights inter. point  M + H  A. B. + H 
Median (M)  H + M  Medians inter. point  A. B. + M 
Angular Bisector (A. B.)  H + A. B.  M + A. B  A. Bisectors inter. point 
Perpendicular Bisector (P. B.)  Height + P. B.  M + P. B.  A. B. + P. B. 
The situation can be further elaborated to discover and generate other interesting loci related to the triangle, if we construct the two intersecting lines of the triangle so that they do not pass through the movable vertex.
The following table should help a lot in organizing the situations design.
Height (H)  Perpendicular Bisector (P. B.)  Median (M)  
Angular Bisector (A. B.)  H +A. B.  P. B. + A. B.  M + A. B. 
Height (H)  P. B. + H  M + H  
Perpendicular Bisector (P. B.)  M + P. B. 
Activity 5: Midpoints of the Sides of a Quadrilateral
Handout 8
The Activity Problem

The Problem Statement

The Problem Conjecture

The Problem Investigation 1

The Problem Investigation 2

The Problem Investigation 3

The Problem Investigation 4
Follow up Problems

Proposed Problem 1: Midpoints of the Sides of a Parallelogram

Proposed Problem 2: Midpoints of the Sides of a Rhombus

Proposed Problem 3: Midpoints of the Sides of a Rectangle

Proposed Problem 4: Midpoints of the Sides of a Square

Proposed Problem 5: Trisecting Points of the Sides of a Quadrilateral

Proposed Problem 6: Trisecting Points of the Sides of a Parallelogram

Proposed Problem 7: Trisecting Points of the Sides of a Rhombus

Proposed Problem 8: Trisecting Points of the Sides of Rectangle

Proposed Problem 9: Trisecting Points of the Sides of Square
Activity 6: Angular Bisectors of a Parallelogram
Handout 9
The Activity Problem
Follow up Problems

Proposed Problem 1: Angular Bisectors of a Rectangle

Proposed Problem 2: Angular Bisectors of an Isosceles Trapezium

Proposed Problem 3: Angular Trisectors of a Parallelogram

Proposed Problem 4: Angular Trisectors of a Rhombus

Proposed Problem 5: Angular Trisectors of a Rectangle

Proposed Problem 6: Angular Trisectors of a Square

Proposed Problem 7: Angular Trisectors of an Isosceles Trapezium

Proposed Problem 8: Medians of a Parallelogram

Proposed Problem 9: Heights of a Parallelogram
Activity 7: Constructing a Parallelogram
Handout 10
Warm up
Parallelogram Properties
Constructions Methods

Construction Method 1  Construct it yourself

Construction Method 2  Construct it yourself

Construction Method 3  Construct it yourself

Construction Method 4  Construct it yourself

Construction Method 5  Construct it yourself

Construction Method 6  Construct it yourself

Construction Method 7  Construct it yourself

Construction Method 8  Construct it yourself

Construction Method 9  Construct it yourself
Activity 8: Constructing a Rhombus
Handout 11
Warm up
Rhombus Properties
Constructions Methods

Construction Method 1  Construct it yourself

Construction Method 2  Construct it yourself

Construction Method 3  Construct it yourself

Construction Method 4  Construct it yourself

Construction Method 5  Construct it yourself

Construction Method 6  Construct it yourself

Construction Method 7  Construct it yourself

Construction Method 8  Construct it yourself

Construction Method 9  Construct it yourself

Construction Method 10  Construct it yourself

Construction Method 11  Construct it yourself
Activity 9: Constructing a Rectangle
Handout 12
Warm up
Rectangle Properties
Constructions Methods

Construction Method 1  Construct it yourself

Construction Method 2  Construct it yourself

Construction Method 3  Construct it yourself

Construction Method 4  Construct it yourself

Construction Method 5  Construct it yourself

Construction Method 6  Construct it yourself

Construction Method 7  Construct it yourself

Construction Method 8  Construct it yourself
Activity 10: Constructing a Square
Handout 13
Warm up
Square Properties
Constructions Methods

Construction Method 1  Construct it yourself

Construction Method 2  Construct it yourself

Construction Method 3  Construct it yourself

Construction Method 4  Construct it yourself

Construction Method 5  Construct it yourself

Construction Method 6  Construct it yourself

Construction Method 7  Construct it yourself

Construction Method 8  Construct it yourself