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1 Bisector of a given angle, using only compass and straight edge.

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1 Bisector of a given angle, using only compass and straight edge.

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https://padlet.com/rdownes/c1

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En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas. En el segundo capítulo sí que se dispone de estas dos herramientas lo que permite concluir las construcciones sensiblemente más rápido. En los dos últimos capítulos, se trabajan construcciones que cuya imposibilidad de realizar con solo regla y compás hizo necesaria la búsqueda de otros métodos o bien la aproximación a la solución.

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Construcciones geométricas con regla y compás

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En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas.

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Introducing concepts about axiomatic systems.

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Welcome to the GeoGebra Geometry App! Learn how to create polygons, visualize transformations, format your constructions, and much more with this collection of video tutorials and applets.

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Welcome to the GeoGebra Geometry App! Learn how to create polygons, visualize transformations, format your constructions, and much more with this collection of video tutorials and applets.

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Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

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This is an interactive course on When you successfully construct the required geometric figure(s) in each exercise, the " geometric constructions , a fascinating topic that has been ignored by the mainstream mathematics education. It is all about drawing geometric figures using specific drawing tools like straightedge, compass and so on. This classical topic in geometry is important because

the foundation of geometry is mostly inspired by what we can do with all these drawing tools, and

it involves a lot of beautiful mathematics that shows the interplay between geometry and algebra.

There are numerous construction exercises in this course. Well done!" message will appear. Prerequisite for this course :

A little bit set theory

High school geometry and algebra

( Note: This GeoGebraBook is an outgrowth of an undergraduate math course that I offer in the Hong Kong University of Science and Technology)

# data[].attributes.attachment_link.description
This is an interactive course on When you successfully construct the required geometric figure(s) in each exercise, the " geometric constructions , a fascinating topic that has been ignored by the mainstream mathematics education. It is all about drawing geometric figures using specific drawing tools like straightedge, compass and so on.

# data[].attributes.attachment_link.readable_text
En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas. En el segundo capítulo sí que se dispone de estas dos herramientas lo que permite concluir las construcciones sensiblemente más rápido. En los dos últimos capítulos, se trabajan construcciones que cuya imposibilidad de realizar con solo regla y compás hizo necesaria la búsqueda de otros métodos o bien la aproximación a la solución.

# data[].attributes.attachment_link.title
Construcciones geométricas con regla y compás

# data[].attributes.attachment_link.description
En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas.

# data[].attributes.attachment_link.readable_text
This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.

# data[].attributes.attachment_link.description
This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.

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Contains various compass and straightedge geometry construction exercises

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Topic:

Angles , Circle , Cone , Congruence , Constructions , Coordinates , Cosine , Cube , Cylinder , Diagrams , Dilation , Equilateral Triangles , Geometry , Incircle or Inscribed Circle , Kite , Straight Lines , Mathematics , Orthocenter , Parallelogram , Perimeter , Plane Figures or Shapes , Planes , Polygons , Prism , Pyramid , Pythagoras or Pythagorean Theorem , Quadrilaterals , Rectangle , Reflection , Rhombus , Right Triangles , Rotation , Scalene Triangles , Secant Line or Secant , Similar Triangles , Similarity Transformation or Similarity , Sine , Solids or 3D Shapes , Sphere , Square , Surface , Symmetry , Tangent Function , Tangent Line or Tangent , Translation , Trapezoid , Triangles , Trigonometric Functions , Trigonometry , Unit Circle , Volume

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Topic: Angles , Circle , Cone , Congruence , Constructions , Coordinates , Cosine , Cube , Cylinder , Diagrams , Dilation , Equilateral Triangles , Geometry , Incircle or Inscribed Circle , Kite , Straight Lines , Mathematics , Orthocenter , Parallelogram , Perimeter , Plane Figures or Shapes

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Katrien Cnudde and Machteld Pensaert of UC Leuven-Limburg created a workshop on doing geometry by folding paper. By folding an A4-sheet, you can create triangles, kites and other figures. More, you can explore properties, calculate angles and dimensions of the figures. This GGbook is a digital version of material of this workshop to assist you when folding. Because, don't just look at the applets, but do the folding yourself and learn geometry by doing!

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Katrien Cnudde and Machteld Pensaert of UC Leuven-Limburg created a workshop on doing geometry by folding paper. By folding an A4-sheet, you can create triangles, kites and other figures. More, you can explore properties, calculate angles and dimensions of the figures. This GGbook is a digital version of material of this workshop to assist you when folding.

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Constructions
https://padlet.com/rdownes/c
https://padlet.com/rdownes/c1
https://padlet.com/rdownes/c2
https://padlet.com/rdownes/c3
https://padlet.com/rdownes/c4
https://padlet.com/rdownes/c5
https://padlet.com/rdownes/c6
https://padlet.com/rdownes/c7
https://padlet.com/rdownes/c8
https://padlet.com/rdownes/c9
https://padlet.com/rdownes/c10
https://padlet.com/rdownes/c11
https://padlet.com/rdownes/c12
https://padlet.com/rdownes/c13
https://padlet.com/rdownes/c14
https://padlet.com/rdownes/c15
https://padlet.com/rdownes/c16
https://padlet.com/rdownes/c17
https://padlet.com/rdownes/c18
https://padlet.com/rdownes/c19
https://padlet.com/rdownes/c20
https://padlet.com/rdownes/c21
https://padlet.com/rdownes/axiom
https://padlet.com/rdownes/theorem
https://padlet.com/rdownes/corollary
https://padlet.com/rdownes/converse
https://padlet.com/rdownes/construction
https://padlet.com/rdownes/induction
https://padlet.com/rdownes/t1
https://padlet.com/rdownes/t2
https://padlet.com/rdownes/t3
https://padlet.com/rdownes/t4
https://padlet.com/rdownes/t5
https://padlet.com/rdownes/t6
https://padlet.com/rdownes/t7
https://padlet.com/rdownes/t8
https://padlet.com/rdownes/t9
https://padlet.com/rdownes/t10
https://padlet.com/rdownes/t11
https://padlet.com/rdownes/t12
https://padlet.com/rdownes/t13
https://padlet.com/rdownes/t14
https://padlet.com/rdownes/t15
https://padlet.com/rdownes/t16
https://padlet.com/rdownes/t17
https://padlet.com/rdownes/t18
https://padlet.com/rdownes/t19
https://padlet.com/rdownes/t20
https://padlet.com/rdownes/t21
https://padlet.com/rdownes/t22
Axioms
https://padlet.com/rdownes/axiom
https://padlet.com/rdownes/a1
https://padlet.com/rdownes/a2
https://padlet.com/rdownes/a3
https://padlet.com/rdownes/a4
https://padlet.com/rdownes/a5
Corollary
https://padlet.com/rdownes/corollary
https://padlet.com/rdownes/cr1
https://padlet.com/rdownes/cr2
https://padlet.com/rdownes/cr3
https://padlet.com/rdownes/cr4
https://padlet.com/rdownes/cr5
https://padlet.com/rdownes/cr6
Constructions
https://padlet.com/rdownes/construction
https://padlet.com/rdownes/c1
https://padlet.com/rdownes/c2
https://padlet.com/rdownes/c3
https://padlet.com/rdownes/c4
https://padlet.com/rdownes/c5
https://padlet.com/rdownes/c6
https://padlet.com/rdownes/c7
https://padlet.com/rdownes/c8
https://padlet.com/rdownes/c9
https://padlet.com/rdownes/c10
https://padlet.com/rdownes/c11
https://padlet.com/rdownes/c12
https://padlet.com/rdownes/c13
https://padlet.com/rdownes/c14
https://padlet.com/rdownes/c15
https://padlet.com/rdownes/c16
https://padlet.com/rdownes/c17
https://padlet.com/rdownes/c18
https://padlet.com/rdownes/c19
https://padlet.com/rdownes/c20
https://padlet.com/rdownes/c21
https://padlet.com/rdownes/c22
Senior Cycle
1. Statistics and Probability
https://padlet.com/rdownes/lcm10
https://padlet.com/rdownes/lcm11
https://padlet.com/rdownes/lcm12
https://padlet.com/rdownes/lcm13
https://padlet.com/rdownes/lcm14
https://padlet.com/rdownes/lcm15
https://padlet.com/rdownes/lcm16
https://padlet.com/rdownes/lcm16h
https://padlet.com/rdownes/lcm17
2. Geometry and Trigonometry
https://padlet.com/rdownes/lcm20
https://padlet.com/rdownes/lcm21
https://padlet.com/rdownes/lcm22
https://padlet.com/rdownes/lcm23
https://padlet.com/rdownes/lcm24
3. Number
https://padlet.com/rdownes/lcm30
https://padlet.com/rdownes/lcm31
https://padlet.com/rdownes/lcm32
https://padlet.com/rdownes/lcm33
https://padlet.com/rdownes/lcm34
4. Algebra
https://padlet.com/rdownes/lcm40
https://padlet.com/rdownes/lcm41
https://padlet.com/rdownes/lcm42
https://padlet.com/rdownes/lcm43
https://padlet.com/rdownes/lcm44
5. Functions
https://padlet.com/rdownes/lcm50
https://padlet.com/rdownes/lcm51
https://padlet.com/rdownes/lcm52
JuniorCycle
Unifying Strand
https://padlet.com/rdownes/u
https://padlet.com/rdownes/u1
https://padlet.com/rdownes/u2
https://padlet.com/rdownes/u3
https://padlet.com/rdownes/u4
https://padlet.com/rdownes/u5
https://padlet.com/rdownes/u6
https://padlet.com/rdownes/u7
https://padlet.com/rdownes/u8
https://padlet.com/rdownes/u9
https://padlet.com/rdownes/u10
https://padlet.com/rdownes/u11
https://padlet.com/rdownes/u12
https://padlet.com/rdownes/u13
Number Strand
https://padlet.com/rdownes/n
https://padlet.com/rdownes/n1
https://padlet.com/rdownes/n2
https://padlet.com/rdownes/n3
https://padlet.com/rdownes/n4
https://padlet.com/rdownes/n5
2. Geometry and Trigonometry
https://padlet.com/rdownes/gt
https://padlet.com/rdownes/gt1
https://padlet.com/rdownes/gt2
https://padlet.com/rdownes/gt3
https://padlet.com/rdownes/gt4
https://padlet.com/rdownes/gt5
https://padlet.com/rdownes/gt6
Algebra and Functions Strand
https://padlet.com/rdownes/af
https://padlet.com/rdownes/af1
https://padlet.com/rdownes/af2
https://padlet.com/rdownes/af3
https://padlet.com/rdownes/af4
https://padlet.com/rdownes/af5
https://padlet.com/rdownes/af6
https://padlet.com/rdownes/af7
Statistics and Probability Strand
https://padlet.com/rdownes/sp
https://padlet.com/rdownes/sp1
https://padlet.com/rdownes/sp2
https://padlet.com/rdownes/sp3

# data[].attributes.attachment_link.readable_text
This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.

# data[].attributes.attachment_link.description
This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.

# data[].attributes.attachment_link.description
The concepts of geometric construction and transformation are central to this GeoGebra Book.

# data[].attributes.attachment_link.readable_text
This is an interactive course on When you successfully construct the required geometric figure(s) in each exercise, the " geometric constructions , a fascinating topic that has been ignored by the mainstream mathematics education. It is all about drawing geometric figures using specific drawing tools like straightedge, compass and so on. This classical topic in geometry is important because

the foundation of geometry is mostly inspired by what we can do with all these drawing tools, and

it involves a lot of beautiful mathematics that shows the interplay between geometry and algebra.

There are numerous construction exercises in this course. Well done!" message will appear. Prerequisite for this course :

A little bit set theory

High school geometry and algebra

( Note: This GeoGebraBook is an outgrowth of an undergraduate math course that I offer in the Hong Kong University of Science and Technology)

# data[].attributes.attachment_link.description
This is an interactive course on When you successfully construct the required geometric figure(s) in each exercise, the " geometric constructions , a fascinating topic that has been ignored by the mainstream mathematics education. It is all about drawing geometric figures using specific drawing tools like straightedge, compass and so on.

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Relation between special lines and points in a triangle. The triangle's vertices can be dragged to form different triangles. Here are some questi...

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Author: Manuel Now

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En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas. En el segundo capítulo sí que se dispone de estas dos herramientas lo que permite concluir las construcciones sensiblemente más rápido. En los dos últimos capítulos, se trabajan construcciones que cuya imposibilidad de realizar con solo regla y compás hizo necesaria la búsqueda de otros métodos o bien la aproximación a la solución.

# data[].attributes.attachment_link.title
Construcciones geométricas con regla y compás

# data[].attributes.attachment_link.description
En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas.

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6. Division of a segment into 2, 3 equal segments, without measuring it.

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6. Division of a segment into 2, 3 equal segments, without measuring it.

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16. Circumcentre and circumcircle of a given triangle, using only straight-edge and compass.

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16. Circumcentre and circumcircle of a given triangle, using only straight-edge and compass.

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https://www.geogebra.org/m/VkWjwK9G

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HL-LC
https://www.geogebra.org/m/VkWjwK9G

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Estimate the orthocenter: Quick intuitive formative assessment.

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2. Perpendicular bisector of a segment, using only compass and straightedge.

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2. Perpendicular bisector of a segment, using only compass and straightedge.

# data[].attributes.body
https://padlet.com/rdownes/c2

# data[].attributes.attachment_link.readable_text
En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas. En el segundo capítulo sí que se dispone de estas dos herramientas lo que permite concluir las construcciones sensiblemente más rápido. En los dos últimos capítulos, se trabajan construcciones que cuya imposibilidad de realizar con solo regla y compás hizo necesaria la búsqueda de otros métodos o bien la aproximación a la solución.

# data[].attributes.attachment_link.title
Construcciones geométricas con regla y compás

# data[].attributes.attachment_link.description
En el primer capítulo se recopilan las construcciones clásicas con solo regla y compás. O sea que la falta de escuadra o cartabón se concreta en que no se puede disponer de las herramientas de GeoGebra para la construcción inmediata de perpendiculares y paralelas.

# data[].attributes.headline
7. Division of a segment into any number of equal segments, without measuring it.

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7. Division of a segment into any number of equal segments, without measuring it.

# data[].attributes.body
HL-JC

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17. Incentre and incircle of a given triangle, using only straight-edge andcompass.

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17. Incentre and incircle of a given triangle, using only straight-edge andcompass.

# data[].attributes.body
https://www.geogebra.org/m/VkWjwK9G

# data[].attributes.attachment_link.readable_text
Goal here: Estimate the location of the triangle's incenter by dragging theLARGE POINT to where you think it lies. You can use the small point to help you out. If you wish to sketch anything in the picture below, you can

Turn on the trace of the small point by selecting the button on the right side.

Turn off the trace of the small point by selecting the button on the right side.

Erase all traces by selecting the Erase Traces button in the lower left corner.

# data[].attributes.attachment_link.description
Goal here: Estimate the location of the triangle's incenter by dragging theLARGE POINT to where you think it lies. You can use the small point to help you out. If you wish to sketch anything in the picture below, you can Turn on the trace of the small point by selecting the button on the right side.

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HL-JC3.                                  Line perpendicular to a given line l, passing through a given point noton l.-                                      

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HL-JC3.                                  Line perpendicular to a given line l, passing through a given point noton l.-                                      

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HL-JC
https://padlet.com/rdownes/c3

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8. Line segment of given length on a given ray.

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8. Line segment of given length on a given ray.

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13. Right-angled triangle, given the length of the hypotenuse and one otherside.

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13. Right-angled triangle, given the length of the hypotenuse and one otherside.

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18. Angle of 60, without using a protractor or set square.

# data[].attributes.subject
18. Angle of 60, without using a protractor or set square.

# data[].attributes.headline
4. Line perpendicular to a given line l, passing through a given point onl.

# data[].attributes.subject
4. Line perpendicular to a given line l, passing through a given point onl.

# data[].attributes.headline
9. Angle of given number of degrees with a given ray as one arm.

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9. Angle of given number of degrees with a given ray as one arm.

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14. Right-angled triangle, given one side and one of the acute angles (sev-eral cases).

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14. Right-angled triangle, given one side and one of the acute angles (sev-eral cases).

# data[].attributes.headline
19. Tangent to a given circle at a given point on it.

# data[].attributes.subject
19. Tangent to a given circle at a given point on it.

# data[].attributes.headline
5. Line parallel to given line, through given point.

# data[].attributes.subject
5. Line parallel to given line, through given point.

# data[].attributes.headline
10. Triangle, given lengths of three sides.

# data[].attributes.subject
10. Triangle, given lengths of three sides.

# data[].attributes.headline
20. Parallelogram, given the length of the sides and the measure of theangles.

# data[].attributes.subject
20. Parallelogram, given the length of the sides and the measure of theangles.

# data[].attributes.body
https://www.geogebra.org/m/bFQRNNXw

# data[].attributes.body
straight-edge: This may be used (together with a pencil) to draw a straight
line passing through two marked points.

# data[].attributes.body
compass: This instrument allows you to draw a circle with a given centre, passing through a given point. It also allows you to take a given segment
[AB], and draw a circle centred at a given point C having radius jABj.

# data[].attributes.body
ruler: This is a straight-edge marked with numbers. It allows you measure
the length of segments, and to mark a point B on a given ray with
vertex A, such that the length jABj is a given positive number. It can
also be employed by sliding it along a set square, or by other methods
of sliding, while keeping one or two points on one or two curves.

# data[].attributes.body
Protractor: This allows you to measure angles, and mark points C such
that the angle \BAC made with a given ray [AB has a given number
of degrees. It can also be employed by sliding it along a line until some
line on the protractor lies over a given point.

# data[].attributes.body
set-squares: You may use these to draw right angles, and angles of 30�,
60�, and 45�. It can also be used by sliding it along a ruler until some
coincidence occurs.

# data[].attributes.body
https://www.geogebra.org/t/centroid

# data[].attributes.headline
2.1 Centroid or BarycenterParent topic:Special Points

# data[].attributes.subject
2.1 Centroid or BarycenterParent topic:Special Points

# data[].attributes.body
The Refelctions of a Line Through the Orthocenter

# data[].attributes.attachment_link.title
The Refelctions of a Line Through the Orthocenter

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Take any line through the orthocenter H of the triangle (drag point E). Reflect this line in the sides of the triangle. The reflections are concur...