## Contents for the exam in September. 3º ESO. Ramón.

Parallel lines

Perpendicular lines.

BISECTORS

Angles.

Copying angles.

Subtracting angles. 1º ESO

Multiplying angles by a real number. 1º ESO

POLYGONS

Triangles.

Definitions.

Classification by sides.

Classification by angles.

Right triangles.

Acute triangles.

Obtuse Triangles.

Oblique triangles.

Circumcircle of a triangle. Circumcentre.

The incentre (incenter) of a triangle. Incircle.

Medians and centroid of a triangle.

Altitude and orthocentre.

Exercises 3º ESO:

Draw an isosceles triangle when you know the unequal angle and the unequal side.

Draw a triangle when you know two sides and the angle they form.

Draw a triangle when you know a side and its two adjacent angles.

Draw a right triangle when you know one leg and its acute adjacent angle.

Draw a right triangle when you know one leg and the hypotenuse *

Draw a right triangle when you know the hypotenuse and the height for that hypotenuse. **

The square. [skwɛər]

Drawing a square when we know the length of the diagonal.

The rectangle.

Drawing rectangles when we know the lengths of two sides:

With the set-squares and the compass.

With the compass and a ruler.

Drawing a rectangle when we know one side and the diagonal.

The rhombus.

Drawing a rhombus when we know the acute angle and its diagonal.

Drawing a rhombus when we know the acute angle and the shorter diagonal (Extra Activity).

The rhomboid.

Drawing a rhomboid when you know both sides and the angle they form.

The trapezoid. [ˈtræpɪzɔɪd]

Drawing a right trapezoid when you know the bases and the height.

Thales´ Theorem.

The division of a segment into n equal parts.

REGULAR POLYGONS

Draw a hexagon and an equilateral triangle inscribed in a circumference.

Draw a regular pengagon inscribed in a circumference.

Draw a heptagon given the side.

Draw a heptagon inscribed in a circunference.

Draw an octagon given the side.

Draw an octagon inscribed in a square.

Draw a regular polygon of any sides inscribed in a circumference: general method for regular polygons.

Stars.

COLOUR

TANGENTS

The concept of tangent lines.

Line tangent to a circumference.

Tangent line to a circumference from a point P.

Common tangents of two circumferences.

Common external or direct tangents.

Common internal or transverse tangents.

Aligned circumferences with the same radius.

Not aligned circumferences with the same radius.

Not aligned circumferences with different radiuses.

Ovals and ovoids.

Spirals.

VISUAL PERCEPTION

Gestalt Theory (see the photocopy).

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