Polygons, circles, square, rectangle, quadrilateral, pentagon, hexagon, decagon, nonagon, prallelogram, trapezium

1. Polygons and circles
Matem´ticas 1o E.S.O.
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Alberto Pardo Milan´s
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2. Alberto Pardo Milan´s
e Polygons and circles

3. Circles
Alberto Pardo Milan´s
e Polygons and circles

4. Circles
What´s a Circle?
A circle is the set of points in a plane that are equidistant from a
given point O.
The distance r from the center is called the radius, and the point
O is called the center.
Twice the radius is known as the diameter d = 2r.
Alberto Pardo Milan´s
e Polygons and circles

5. Triangles
Alberto Pardo Milan´s
e Polygons and circles

6. 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 to
be 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 one
angle that is greater than 90o , an acute triangle has all three
angles less than 90o .
Alberto Pardo Milan´s
e Polygons and circles

7. Triangles
Equilateral, Isosceles or Scalene?
A triangle with all sides equal is called equilateral. A triangle with
two sides equal is called isosceles. A triangle with all sides a
different length is called scalene.
An equilateral triangle has all three sides the same length, an
isosceles triangle has two sides with the same length, a scalene
triangle has all three sides different lengths.
An equilateral triangle has all three angles the same, an isosceles
triangle has two equal angles, a scalene triangle has all three angles
unequal.
Alberto Pardo Milan´s
e Polygons and circles

8. Triangles
Legs and Hypotenuse. Pythagorean theorem.
The sides of a triangle are given special names in the case of a
right triangle, with the side opposite the right angle being named
the hypotenuse and the other two sides being known as the legs.
Pythagorean theorem: for a right triangle with legs a and b and
hypotenuse h: h2 = a2 + b2 .
Alberto Pardo Milan´s
e Polygons and circles

9. Polygons
Alberto Pardo Milan´s
e Polygons and circles

10. 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 Milan´s
e Polygons and circles

11. Regular Polygons
Alberto Pardo Milan´s
e Polygons and circles

12. Regular Polygons
All sides and all angles are equal.
In a polygon, if all sides and angles are equal, the polygon is called
regular.
Every regular triangle is an equilateral triangle.
A regular quadrilateral is called a square.
Alberto Pardo Milan´s
e Polygons and circles

13. Regular Polygons
Radius and apothem of Regular Polygons.
For a regular polygon, the radius R is the distance from the
center to a vertex of the polygon and the apothem is the distance
r from the center to a side of the polygon.
Alberto Pardo Milan´s
e Polygons and circles

14. Exercises
Alberto Pardo Milan´s
e Polygons and circles