Suggested
Enrichment Program Using Cinderella (DGS)
© 2007-2008 Mohamed El-Demerdash
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
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The Sum of Measures of the Interior Angles of a Triangle
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The Sum of the Accumulative Angles at a Point
The Activity Problem
Follow up Problems
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Proposed Problem 1: Four Triangles Equal in Perimeter
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Proposed Problem 2: Area Relationship
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Proposed Problem 3: Four Congruent Triangles
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Proposed Problem 4: Five Similar Triangles
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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
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Conjecture 1: The Relationship between the Line of Centers and the Common Chord
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Conjecture 2: Quadrilateral Kite
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Conjecture 3: Congruent Triangle
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Conjecture 4: The Line of Centers as an Angular Bisector
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Conjecture 5: Parallelism Relationship
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Conjecture 6: Similar Triangles
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Conjecture 7: Rectangle
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Conjecture 8: Area Relationship 1
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Conjecture 9: Area Relationship 2
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Conjecture 10: Area Relationship 3
Activity 3: Developing Macro-constructions
Handout 6
Macro-constructions
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Perpendicular Bisector
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Circum-center Point of a Triangle
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In-center Point of a Triangle
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Orthocenter Point of a Triangle
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Center of Mass or Centroid Point of a Triangle
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Euler Line of a Triangle
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Euler Ratio of a Triangle
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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
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The Locus of the Intersection Point of Medians of a Triangle
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The Locus of the Intersection Point of Angular Bisectors of the Interior Angles of a Triangle
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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
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The Problem Statement
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The Problem Conjecture
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The Problem Investigation 1
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The Problem Investigation 2
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The Problem Investigation 3
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The Problem Investigation 4
Follow up Problems
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Proposed Problem 1: Midpoints of the Sides of a Parallelogram
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Proposed Problem 2: Midpoints of the Sides of a Rhombus
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Proposed Problem 3: Midpoints of the Sides of a Rectangle
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Proposed Problem 4: Midpoints of the Sides of a Square
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Proposed Problem 5: Trisecting Points of the Sides of a Quadrilateral
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Proposed Problem 6: Trisecting Points of the Sides of a Parallelogram
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Proposed Problem 7: Trisecting Points of the Sides of a Rhombus
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Proposed Problem 8: Trisecting Points of the Sides of Rectangle
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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
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Proposed Problem 1: Angular Bisectors of a Rectangle
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Proposed Problem 2: Angular Bisectors of an Isosceles Trapezium
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Proposed Problem 3: Angular Trisectors of a Parallelogram
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Proposed Problem 4: Angular Trisectors of a Rhombus
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Proposed Problem 5: Angular Trisectors of a Rectangle
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Proposed Problem 6: Angular Trisectors of a Square
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Proposed Problem 7: Angular Trisectors of an Isosceles Trapezium
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Proposed Problem 8: Medians of a Parallelogram
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Proposed Problem 9: Heights of a Parallelogram
Activity 7: Constructing a Parallelogram
Handout 10
Warm up
Parallelogram Properties
Constructions Methods
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Construction Method 1 | Construct it yourself
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Construction Method 2 | Construct it yourself
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Construction Method 3 | Construct it yourself
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Construction Method 4 | Construct it yourself
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Construction Method 5 | Construct it yourself
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Construction Method 6 | Construct it yourself
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Construction Method 7 | Construct it yourself
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Construction Method 8 | Construct it yourself
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Construction Method 9 | Construct it yourself
Activity 8: Constructing a Rhombus
Handout 11
Warm up
Rhombus Properties
Constructions Methods
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Construction Method 1 | Construct it yourself
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Construction Method 2 | Construct it yourself
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Construction Method 3 | Construct it yourself
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Construction Method 4 | Construct it yourself
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Construction Method 5 | Construct it yourself
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Construction Method 6 | Construct it yourself
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Construction Method 7 | Construct it yourself
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Construction Method 8 | Construct it yourself
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Construction Method 9 | Construct it yourself
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Construction Method 10 | Construct it yourself
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Construction Method 11 | Construct it yourself
Activity 9: Constructing a Rectangle
Handout 12
Warm up
Rectangle Properties
Constructions Methods
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Construction Method 1 | Construct it yourself
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Construction Method 2 | Construct it yourself
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Construction Method 3 | Construct it yourself
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Construction Method 4 | Construct it yourself
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Construction Method 5 | Construct it yourself
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Construction Method 6 | Construct it yourself
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Construction Method 7 | Construct it yourself
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Construction Method 8 | Construct it yourself
Activity 10: Constructing a Square
Handout 13
Warm up
Square Properties
Constructions Methods
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Construction Method 1 | Construct it yourself
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Construction Method 2 | Construct it yourself
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Construction Method 3 | Construct it yourself
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Construction Method 4 | Construct it yourself
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Construction Method 5 | Construct it yourself
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Construction Method 6 | Construct it yourself
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Construction Method 7 | Construct it yourself
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Construction Method 8 | Construct it yourself