# data[].attributes.attachment_link.title
Fiche préparation séquence CLIL - Programme de construction en géométrie

# data[].attributes.headline
Rituel - Géométrie - Programme construction

# data[].attributes.subject
Rituel - Géométrie - Programme construction

# data[].attributes.attachment_link.title
Fiche SEANCE CLIL - Programme de construction en géométrie, séance 3

# data[].attributes.attachment_link.title
g%C3%A9ometrie devinettes associer une consigne et une figue - Google Search

# data[].attributes.attachment_link.readable_text
In this mini-lesson, we will explore the world of geometric constructions in math. You will get to learn about the way to construct perpendicular bisector, angle bisector, parallel lines and other interesting facts around the topic. You can try your hand at solving a few interesting practice questions at the end of the page.

Austin is a civil engineer.

He needs an accurate map to construct a building and design the tools.

To draw such figures, he uses some basic geometrical instruments like a graduated scale, a pair of set-squares, divider, compass, and ruler.

We don't want you to worry, and get your geometric instruments ready as we, at Cuemath, are here to help you understand the geometric constructions in a clear way.

In this short lesson, we will learn some basic geometric constructions.

Geometric construction is the process of drawing a geometrical figure using two geometrical instruments, a compass, and a ruler.

We use a compass to draw arcs and circles and mark off equal lengths.

We use a ruler to draw line segments and measure their lengths.

How To Construct Perpendicular Bisector?

To carry out this construction, we will use the fact that any point on the perpendicular bisector of a line segment is equidistant from the two end-points of the line segment.

Suppose we have a line segment \(\overline{AB}\).

The steps in the construction are outlined below.

Step 1: Taking A and B as centers, and a radius of more than half of \(\overline{AB}\), draw arcs on both sides of \(\overline{AB}\), to intersect each other, as shown below.

The reason you require the radius of your arcs to be more than half of \(\overline{AB}\) is that if the radius is less than half of \(\overline{AB}\), the arcs will not intersect (try it!).

Step 2: Let the two points of the intersection so obtained be P and Q. Draw a line through P and Q. This is the required perpendicular bisector.

Here, POQ is the perpendicular bisector of \(\overline{AB}\).

You can visualize these steps in the simulation below by clicking the 'GO' button.

Isn't it interesting to realize the fact that these orange and green lines will go on forever but will never meet?

These two lines are parallel to each other.

We will learn how to construct parallel lines using a ruler and a compass.

Let \(\overleftrightarrow{AB}\) be a line and P be a point outside the line \(\overleftrightarrow{AB}\).

Step 1: Draw a transversal through the point P intersecting the line \(\overleftrightarrow{AB}\), say at X.

Step 2: Taking X as a center and any radius, draw an arc intersecting the segment \(\overline{PX}\) at M and \(\overleftrightarrow{AB}\) at point N.

Step 3: Now, taking P as a center and the same radius, draw an arc EF intersecting the segment \(\overline{PX}\) at Q.

Step 4: Taking Q as a center and same radius, draw an arc intersecting the arc EF at R.

Step 5: Join R and P and extend it on both sides to draw the line \(\overleftrightarrow{CD}\).

Here, the line \(\overleftrightarrow{CD}\) is parallel to the line \(\overleftrightarrow{AB}\).

Experiment with the simulation below to visualize this process by clicking the 'GO' button.

How To Construct an Angle Bisector?

Suppose we have \(\angle PQR\) and we want to bisect this angle.

Follow the steps of construction mentioned below:

1. Let Q be the center and with any radius, draw an arc intersecting the ray \(\overrightarrow{QP}\) and \(\overrightarrow{QR}\), say at the points E and D respectively.

2. Now, taking D and E as centers and the same radius, draw arcs intersecting each other say at F.

3. Draw the ray \(\overrightarrow{QF}\).

Here, \(\overrightarrow{QP}\) is the angle bisector of \(\angle PQR\).

Use the simulation below to visualize the steps of construction for angle bisector by clicking the 'GO' button.

The green and blue lines are parallel, and M and N are points on the green and blue lines respectively.

If the shortest distance from M to the blue line is 6 units.

What will be the shortest distance from N to the green line?

The given lines are parallel, so they are equidistant throughout.

This means that the perpendicular distance from M to the blue line is equal to the perpendicular distance from N to the green line. Hence, this distance is equal to 6 units.

In fact, the shortest distance between the two lines is the perpendicular distance between them.

So, the shortest distance from N to the green line is 6 units.

Ryan is flying a kite.

The kite has two angles bisected as shown below.

Can you find the measures of the angles \(\angle EKI\) and \(\angle ITE\)?

The angles \(\angle EKI\) and \(\angle ITE\) are bisected by the line \(\overleftrightarrow{KT}\).

\(\overleftrightarrow{KT}\) divides the angles \(\angle EKI\) and \(\angle ITE\) in two equal angles respectively.

Thus,

\(\angle EKI=2\times 45^{\circ}=90^{\circ}\) and

\(\angle ITE=2\times 27^{\circ}=54^{\circ}\)

\(\therefore\) \(\angle EKI=90^{\circ}\) and \(\angle ITE=54^{\circ}\).

Ms. Amy asked Mia to justify the construction of a perpendicular bisector of a line segment.

Can you help her justify this?

In \(\Delta PAQ\) and \(\Delta PBQ\):

1. PA = PB (arcs of equal radius)

2. QA = QB (again, arcs of equal radius)

3. PQ = PQ (common)

By the SSS criterion, the two triangles are congruent, which means that \(\angle APO\) = \(\angle BPO\).

In \(\Delta APO\) with \(\Delta BPO\):

1. PA = PB (arcs of equal radius)

2. \(\angle APO\) = \(\angle BPO\) (just shown)

3. PO = PO (common)

By the SAS criterion, the two triangles are congruent, which means that AO = BO, and also:

\(\angle AOP\) = \(\angle BOP\) = \(\dfrac{1}{2}180^0 = 90^0\)

\(\therefore\), POQ is the perpendicular bisector of AB.

\(\angle PQR\) is divided into different angles.

Can you determine the angle bisector of \(\angle PQR\)?

Notice that,

\[\begin{align}\angle PQT&=\angle PQV + \angle VQT \\&= 50^{\circ}+ 10^{\circ}\\&= 60^{\circ}\end{align}\]

\[\begin{align}\angle TQR&= \angle TQS + \angle SQR \\ &= 35^{\circ}+ 25^{\circ}\\&= 60^{\circ}\end{align}\]

This means that \(\angle PQT=\angle TQR\).

So, ray QT is the angle bisector of \(\angle PQR\).

Be careful while doing geometric constructions.

Here are a few tips and tricks for you to follow while doing construction.

# data[].attributes.attachment_link.title
Geometric constructions-Steps and solved examples - Cuemath

# data[].attributes.attachment_link.description
In this mini-lesson, we will explore the world of geometric constructions in math. You will get to learn about the way to construct perpendicular bisector, angle bisector, parallel lines and other interesting facts around the topic. You can try your hand at solving a few interesting practice questions at the end of the page.

# data[].attributes.attachment_link.title
Fiche SEANCE CLIL - Programme de construction en géométrie, séance 3

# data[].attributes.attachment_link.title
Fiche préparation séquence CLIL - Programme de construction en géométrie

# data[].attributes.attachment_link.readable_text
Pierre CALO gero est un artiste français, autodidacte, qui pratique le dessin et la peinture depuis l'âge de vingt ans. Il a débuté par une période figurative avant d'adopter l'abstraction comme mode principal d'expression. Il a expérimenté les techniques et les supports les plus variés. Il a appris la gravure et l'impression dans l'atelier parisien du peintre Henri Goetz.

De nombreuses manifestations jalonnent les différentes étapes de son parcours artistique. Il a participé à de multiples expositions individuelles et collectives en France ou à l'étranger. En 2015 il a exposé une partie de son travail en Chine avec un groupe d'artistes français. En 2017 il a participé au Salon d'Automne à Paris. Il a illustré une édition pour l'éditeur Fata Morgana à Montpellier en 2001.

Sa démarche artistique s'inscrit dans un espace en deux dimensions : La couleur et la texture, le geste et le dessin. Il fabrique lui même ses couleurs à base de pigments ainsi que ses matières. Sa pratique repose sur plusieurs vecteurs: empreintes, projections, gaufrages, collages. Il utilise principalement l'acrylique, le sable, l'encre de Chine.

Son inspiration repose sur un besoin permanent de peindre et trouve ses sources dans la nature ou dans la photographie qu'il pratique également. Il représente des formes géométriques ou construites ou des projections gestuelles basées sur le souffle et la concentration.

Sa peinture reste non figurative, elle est une invitation au voyage intérieur, elle conjugue rigueur et hasard, réel et imaginaire, la couleur et la lumière jaillissent comme une source en permanent renouvellement et l'expression d'une grande liberté

Autodidacte qui dessine et qui peint depuis l'âge de vingt ans. A appris la gravure dans l'Atelier du peintre Henri Goetz à Paris.
Expositions Collectives :
Salon des Artistes Indépendants

Salon d'Automne

Galerie Saphira Ventura New York

Galerie Bogart Bruxelles

Centre d'Echanges France Chine à Pékin et ShangaÏ .

Expositions Individuelles :

Juin 2020 : Exposition Galerie DavidCha 51 avenue Montaigne Paris 8

2018 : Galerie Mona Lisa Paris

2011 : Galerie Art Présent

1996 : Galerie des Grands Augustins Paris

Fata Morgana Montpellier

Frac Ile de France

Exposition Individuelle Juin 2021 Galerie Mona Lisa 32 rue de Varenne 75007 Paris Art Shopping Carousel du Louvre Vente aux enchères Maitre Millon 23 Octobre 2021

# data[].attributes.attachment_link.title
Galerie de l'artiste CALO - KAZoART, Galerie d'art en ligne

# data[].attributes.attachment_link.description
Pierre CALO gero est un artiste français, autodidacte, qui pratique le dessin et la peinture depuis l'âge de vingt ans. Il a débuté par une période figurative avant d'adopter l'abstraction comme mode principal d'expression. Il a expérimenté les techniques et les supports les plus variés.

# data[].attributes.attachment_link.title
Expo Centre Pompidou - cercles-et-carres-2013

# data[].attributes.attachment_link.title
Séquence géométrie - lexique - structure de phrases - verbes

# data[].attributes.attachment_link.title
Fiche préparation séances 1 et 2 + 2b CLIL

# data[].attributes.headline
Mini-fichier : programmes de construction

# data[].attributes.subject
Mini-fichier : programmes de construction

# data[].attributes.attachment_link.description
Learn how to construct a Perpendicular to a Point on a Line using just a compass and a straightedge

# data[].attributes.attachment_link.authors[].name
The Singing Walrus - English Songs For Kids

# data[].attributes.attachment_link.title
Shapes song for kids | The Singing Walrus

# data[].attributes.body
Sitographie et ressources pour différentes matières dont les mathématiques (envoyée par Amélie Jordan).

# data[].attributes.headline
Atelier Vocabulaire Géométrique (en français)

# data[].attributes.subject
Atelier Vocabulaire Géométrique (en français)

# data[].attributes.body
Atelier à adapter en anglais ou à utiliser pour vérifier l'acquisition des compétences.