BASIC GEOMETRIC CONSTRUCTIONS
Geometric Constructions Compass
"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil. This is the "pure" form of geometric construction: no numbers involved!
Click the link below
SET SQUARE INTRODUCTION 30/60/90 &45 DEGREES
VíDEO
SET SQUARES.
SET SQUARES (tools) a thin flat piece of plastic, metal, etc, in the shape of a right-angled triangle, used in technical drawing.
RIGHT ISOSCELES TRIANGLE
RIGHT SCALENE TRIANGLE
SET SQUARES.
SET SQUARES are used to draw angles of 90º, 45º, 30º, 60º or a combination of these angles.
RIGHT ISOSCELES TRIANGLE
RIGHT SCALENE TRIANGLE
Drawing parallel and perpendicular lines.
PARALLEL LINES Look at where the 45º and 60º/30º set squares are positioned in the picture on the left. This position enables us to draw parallel lines. The 60º/30º set square stays in the same place, whilst the 45º set square slides down the page to draw lines at different horizontal positions. These lines are therefore parallel.
Drawing parallel and perpendicular lines.
PERPENDICULAR LINES To draw perpendicular lines, you simply have to rotate the 45º set square, as shown in the picture on the right. Meanwhile, the 60º/30º set square stays in its original position. When you move the 45º set square, you can draw lines that are parallel to one another and perpendicular to the original lines.
VíDEO
HOW TO DRAW PARALLEL AND PERPENDICULAR LINES USING SET SQUARES.
Construction of angle- Using Set Squares
VíDEO
SET SQUARES.
VíDEO
CONSTRUCTION OF ANGLE-USING SET SQUARES
PIET MONDRIAN
VíDEO
VíDEO
Deconstructing Mondrian: The story behind an iconic design.
Artist Piet Mondrian is known today for his patterns of black lines and bold, primary colors. But he started out painting classic Dutch landscapes. An exhibit at the Gemeentemuseum in The Hague traces the artist's path to abstraction.
VíDEO
Can you solve the MONDRIAN squares riddle?
VíDEO
Piet Mondrian's Artistic Evolution.
BASIC GEOMETRIC CONSTRUCTIONS
LINE SEGMENT - Copy a line segment - Add line segments - Substract line segments - Line segment bisector and right angle.
CIRCUMFERENCE, CIRCLE AND ARC
SECTION
ANGLES - Same (congruent angle) -Add angles -Substract angles - Angle bisector
THALES THEOREM -Cut a line segment into n equal segments.
CONSTRUCTIONES GEOMÉTRICAS BÁSICAS
SEGMENTO - Copia un segmento dado - Suma de segmentos - Resta de segmentos - Mediatriz.
CIRCUNFERENCIA, CÍRCULO Y ARCO.
SECTION
ÁNGULOS - Copia de ángulos -Suma de ángulos -Resta de ángulos - Bisectriz
TEOREMA DE THALES. - División de un segmento en partes iguales
CLICK AND WATCH THIS VIDEO
SEGMENTO
LINE SEGMENT
The part of a line that connects two points.It is the shortest distance between the two points.
Es la parte de línea que une dos puntos.Es la distancia más corta entre dos puntos.
Extremos del segmento
SECTION
SEGMENTO
LINE SEGMENT
The part of a line that connects two points.It is the shortest distance between the two points.
Es la parte de línea que une dos puntos.Es la distancia más corta entre dos puntos.
Extremos del segmento
SECTION
- LINE SEGMENT BISECTOR AND RIGHT ANGLES.
- COPY A LINE SEGMENT
- Copia un segmento
- ADD LINE SEGMENTS.
- Suma de segmentos.
- SUBSTRACT LINE SEGMENTS.
- Resta de segmentos.
- LINE SEGMENT BISECTOR AND RIGHT ANGLES.
- Mediatriz y ángulos rectos
- SAME (CONGRUENT ANGLE)
- Mismo ángulo
- ADD ANGLES
- Suma de ángulos
- SUBSTRACT ANGLES
- Resta de ángulos
ANGLES
- Acute Angle is less than 90°
- Right Angle is 90° exactly
- Obtuse Angle is greater than 90° but
less than 180°
- Straight Angle is 180° exactly
- Reflex Angle is greater than 180°
- Full Rotation is 360° exactly3
ANGLES
agudo
cóncavo
recto
obtuso
llano
completo
- Ángulo agudo, menor de 90°
- Ángulo recto, 90°
- Ángulo obtuso, es mayor de 90º pero menor de 180º.
- Ángulo llano, 180º
- Ángulo cóncavo, mayor de 180°
- Ángulo completo, 360°
ANGLES
ACTIVITY: ANGLES: ACUTE, OBTUSE...
ANGLES
ACTIVITY
ANGLES
Complete the table by filling in the size of each angle described.
ACTIVITY
ANGLES. Using the protractor
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
COMPLEMENTARY ANGLES
QUIZ
SUPLEMENTARY ANGLES
QUIZ
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 1 o'clock?
¿Qué ángulo forman las manillas de un reloj a la una?
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 1 o'clock?
360° ÷ 12 = 30°
So the angle between the hands of a clock at 1 o'clock is 30° .
360° ÷ 12 = 30°, por tanto, el ángulo entre las manillas del reloj a la una es de 30° .
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 2:30?
Cuál es el ángulo entre las manillas de un reloj a las 2:30?
ACTIVITY CLOCKS AND ANGLES
- The angle between the 5 and the 6 is 30°
- The angle between the 4 and the 5 is 30°
- The angle between the 3 and the 4 is 30°
- The remaining angle is ½ × 30° = 15°
So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105°
SECTION
What is the angle between the hands of a clock at 2:30?
- El ángulo entre las 5 y las 6 es de 30º
- El ángulo entre las 4 y las 5 es de 30º
- El ángulo entre las 3 y las 4 es de 30º
- El ángulo restante es la mitad de 30º (15º)
- Por tanto, el ángulo entre las manillas del reloj a las 2:30 = 30º+30º+30º+15º=105º
CIRCUNFERENCIA Y CÍRCULO
CIRCUMFERENCE CIRCLE
SECTION
CIRCLE is the name of a two-dimensional shape and a one-dimensional curve.CIRCUMFERENCE is the perimeter of the circle. In other words it is the length of the boundary of circle. The shape has a certain property that any point lying on the shape is always at a constant distance from a point called centre.
El CÍRCULO es una figura plana formada por una circunferencia y su interior. La CIRCUNFERENCIA es una línea curva, cerrada y plana cuyos puntos están a la misma distancia del centro.
CLICK AND WATCH THIS VIDEO
PARTES DE LA CIRCUNFERENCIA
PARTS OF THE CIRCLE
Tangente
Secante
Cuerda
SECTION
Diámetro
Radio
Arco
A line that "just touches" the circle as it passes by is called a TANGENT. A line that cuts the circle at two points is called a SECANT. A line segment that goes from one point to another on the circle's circumference is called a CHORD. If it passes through the center it is called a DIAMETER. The RADIUS of a circle is the length of the line from the center to any point on its edge.A part of the circumference is called an ARC.
Tangente: recta que solo tiene un punto en común con la circunferencia.Secante: recta que corta a la circunferencia en dos puntos. Cuerda: segmento que une dos puntos de la circunferencia. Diámetro: recta que une dos puntos de la circunferencia pasando por el centro. Arco es cada parte en que una cuerda divide a una circunferencia.
RELATIVE POSITION OF TWO CIRCLES
SECTION
POSICIONES RELATIVAS DE DOS CIRCUNFERENCIAS
SECTION
USING THE COMPASS
CONSTRUCTING CIRCLES WITH A COMPASS
CONSTRUCTING CIRCLES WITH A COMPASS
CIRCLES ON CIRCLES
CIRCLES ON CIRCLES
USING CIRCLES TO DRAW OTHER FIGURES
FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN
FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN
Dividing a segment into several equal parts
We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler. By using a compass and straightedge construction, we do this without measuring the line.
BASIC GEOMETRIC CONSTRUCTIONS
Alicia Suárez López
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Transcript
BASIC GEOMETRIC CONSTRUCTIONS
Geometric Constructions Compass "Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil. This is the "pure" form of geometric construction: no numbers involved!
Click the link below
SET SQUARE INTRODUCTION 30/60/90 &45 DEGREES
VíDEO
SET SQUARES.
SET SQUARES (tools) a thin flat piece of plastic, metal, etc, in the shape of a right-angled triangle, used in technical drawing.
RIGHT ISOSCELES TRIANGLE
RIGHT SCALENE TRIANGLE
SET SQUARES.
SET SQUARES are used to draw angles of 90º, 45º, 30º, 60º or a combination of these angles.
RIGHT ISOSCELES TRIANGLE
RIGHT SCALENE TRIANGLE
Drawing parallel and perpendicular lines.
PARALLEL LINES Look at where the 45º and 60º/30º set squares are positioned in the picture on the left. This position enables us to draw parallel lines. The 60º/30º set square stays in the same place, whilst the 45º set square slides down the page to draw lines at different horizontal positions. These lines are therefore parallel.
Drawing parallel and perpendicular lines.
PERPENDICULAR LINES To draw perpendicular lines, you simply have to rotate the 45º set square, as shown in the picture on the right. Meanwhile, the 60º/30º set square stays in its original position. When you move the 45º set square, you can draw lines that are parallel to one another and perpendicular to the original lines.
VíDEO
HOW TO DRAW PARALLEL AND PERPENDICULAR LINES USING SET SQUARES.
Construction of angle- Using Set Squares
VíDEO
SET SQUARES.
VíDEO
CONSTRUCTION OF ANGLE-USING SET SQUARES
PIET MONDRIAN
VíDEO
VíDEO
Deconstructing Mondrian: The story behind an iconic design.
Artist Piet Mondrian is known today for his patterns of black lines and bold, primary colors. But he started out painting classic Dutch landscapes. An exhibit at the Gemeentemuseum in The Hague traces the artist's path to abstraction.
VíDEO
Can you solve the MONDRIAN squares riddle?
VíDEO
Piet Mondrian's Artistic Evolution.
BASIC GEOMETRIC CONSTRUCTIONS
LINE SEGMENT - Copy a line segment - Add line segments - Substract line segments - Line segment bisector and right angle.
CIRCUMFERENCE, CIRCLE AND ARC
SECTION
ANGLES - Same (congruent angle) -Add angles -Substract angles - Angle bisector
THALES THEOREM -Cut a line segment into n equal segments.
CONSTRUCTIONES GEOMÉTRICAS BÁSICAS
SEGMENTO - Copia un segmento dado - Suma de segmentos - Resta de segmentos - Mediatriz.
CIRCUNFERENCIA, CÍRCULO Y ARCO.
SECTION
ÁNGULOS - Copia de ángulos -Suma de ángulos -Resta de ángulos - Bisectriz
TEOREMA DE THALES. - División de un segmento en partes iguales
CLICK AND WATCH THIS VIDEO
SEGMENTO
LINE SEGMENT
The part of a line that connects two points.It is the shortest distance between the two points.
Es la parte de línea que une dos puntos.Es la distancia más corta entre dos puntos.
Extremos del segmento
SECTION
SEGMENTO
LINE SEGMENT
The part of a line that connects two points.It is the shortest distance between the two points.
Es la parte de línea que une dos puntos.Es la distancia más corta entre dos puntos.
Extremos del segmento
SECTION
ANGLES
ANGLES
agudo
cóncavo
recto
obtuso
llano
completo
ANGLES
ACTIVITY: ANGLES: ACUTE, OBTUSE...
ANGLES
ACTIVITY
ANGLES
Complete the table by filling in the size of each angle described.
ACTIVITY
ANGLES. Using the protractor
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
ANGLES. How to use a protractor to measure an angle.
COMPLEMENTARY ANGLES
QUIZ
SUPLEMENTARY ANGLES
QUIZ
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 1 o'clock?
¿Qué ángulo forman las manillas de un reloj a la una?
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 1 o'clock?
360° ÷ 12 = 30° So the angle between the hands of a clock at 1 o'clock is 30° .
360° ÷ 12 = 30°, por tanto, el ángulo entre las manillas del reloj a la una es de 30° .
ACTIVITY CLOCKS AND ANGLES
SECTION
What is the angle between the hands of a clock at 2:30?
Cuál es el ángulo entre las manillas de un reloj a las 2:30?
ACTIVITY CLOCKS AND ANGLES
- The angle between the 5 and the 6 is 30°
- The angle between the 4 and the 5 is 30°
- The angle between the 3 and the 4 is 30°
- The remaining angle is ½ × 30° = 15°
So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105°SECTION
What is the angle between the hands of a clock at 2:30?
CIRCUNFERENCIA Y CÍRCULO
CIRCUMFERENCE CIRCLE
SECTION
CIRCLE is the name of a two-dimensional shape and a one-dimensional curve.CIRCUMFERENCE is the perimeter of the circle. In other words it is the length of the boundary of circle. The shape has a certain property that any point lying on the shape is always at a constant distance from a point called centre.
El CÍRCULO es una figura plana formada por una circunferencia y su interior. La CIRCUNFERENCIA es una línea curva, cerrada y plana cuyos puntos están a la misma distancia del centro.
CLICK AND WATCH THIS VIDEO
PARTES DE LA CIRCUNFERENCIA
PARTS OF THE CIRCLE
Tangente
Secante
Cuerda
SECTION
Diámetro
Radio
Arco
A line that "just touches" the circle as it passes by is called a TANGENT. A line that cuts the circle at two points is called a SECANT. A line segment that goes from one point to another on the circle's circumference is called a CHORD. If it passes through the center it is called a DIAMETER. The RADIUS of a circle is the length of the line from the center to any point on its edge.A part of the circumference is called an ARC.
Tangente: recta que solo tiene un punto en común con la circunferencia.Secante: recta que corta a la circunferencia en dos puntos. Cuerda: segmento que une dos puntos de la circunferencia. Diámetro: recta que une dos puntos de la circunferencia pasando por el centro. Arco es cada parte en que una cuerda divide a una circunferencia.
RELATIVE POSITION OF TWO CIRCLES
SECTION
POSICIONES RELATIVAS DE DOS CIRCUNFERENCIAS
SECTION
USING THE COMPASS
CONSTRUCTING CIRCLES WITH A COMPASS
CONSTRUCTING CIRCLES WITH A COMPASS
CIRCLES ON CIRCLES
CIRCLES ON CIRCLES
USING CIRCLES TO DRAW OTHER FIGURES
FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN
FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN
Dividing a segment into several equal parts
We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler. By using a compass and straightedge construction, we do this without measuring the line.