Polygons and circles

Matematicas 1o E.S.O.Alberto Pardo Milanes

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Alberto Pardo Milanes Polygons and circles

Circles

Alberto Pardo Milanes Polygons and circles

Circles

What´s a Circle?

A circle is the set of points in a plane that are equidistant from agiven point O.

The distance r from the center is called the radius, and the pointO is called the center.

Twice the radius is known as the diameter d = 2r.

Alberto Pardo Milanes Polygons and circles

Triangles

Alberto Pardo Milanes Polygons and circles

Triangles

What´s a Triangle? Acute, Obtuse or Right?

A triangle is a closed plane figure with three sides.

If all three of the angles of a triangle are all acute then is said tobe acute.A triangle having an obtuse angle is called an obtuse triangle.A triangle with a right angle is called right.A right triangle has one 90o angle, an obtuse triangle has oneangle that is greater than 90o, an acute triangle has all threeangles less than 90o.

Alberto Pardo Milanes Polygons and circles

Triangles

Equilateral, Isosceles or Scalene?

A triangle with all sides equal is called equilateral. A triangle withtwo sides equal is called isosceles. A triangle with all sides adifferent length is called scalene.An equilateral triangle has all three sides the same length, anisosceles triangle has two sides with the same length, a scalenetriangle has all three sides different lengths.

An equilateral triangle has all three angles the same, an isoscelestriangle has two equal angles, a scalene triangle has all three anglesunequal.

Alberto Pardo Milanes Polygons and circles

Triangles

Legs and Hypotenuse. Pythagorean theorem.

The sides of a triangle are given special names in the case of aright triangle, with the side opposite the right angle being namedthe hypotenuse and the other two sides being known as the legs.

Pythagorean theorem: for a right triangle with legs a and b andhypotenuse h: h2 = a2 + b2.

Alberto Pardo Milanes Polygons and circles

Polygons

Alberto Pardo Milanes Polygons and circles

Polygons

A Figure with “many angles”

A polygon is a closed plane figure with n sides. The word“polygon” derives from the Greek “poly”, meaning “many”, and“gonia”, meaning “angle”.A triangle is a polygon with three sides.A quadrilateral is a polygon with four sides.

Name Triangle Quadrilateral Pentagon Hexagon

Sides/angles 3 4 5 6

Name Heptagon Octagon Nonagon Decagon

Sides/angles 7 8 9 10

Alberto Pardo Milanes Polygons and circles

Regular Polygons

Alberto Pardo Milanes Polygons and circles

Regular Polygons

All sides and all angles are equal.

In a polygon, if all sides and angles are equal, the polygon is calledregular.Every regular triangle is an equilateral triangle.A regular quadrilateral is called a square.

Alberto Pardo Milanes Polygons and circles

Regular Polygons

Radius and apothem of Regular Polygons.

For a regular polygon, the radius R is the distance from thecenter to a vertex of the polygon and the apothem is the distancer from the center to a side of the polygon.

Alberto Pardo Milanes Polygons and circles

Exercises

Alberto Pardo Milanes Polygons and circles