GEOMETRICAL SHAPES - WordPress.com€¦ · PYTHAGORAS’ THEOREM In a right triangle, its hypotenuse is the side opposite of the right angle. The other two sides are called legs

GEOMETRICAL SHAPES

www.matematicasalmudena.com Almudena Casares Fernández

POLYGONS

VIDEO

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x=4&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n

A polygon is a flat shape completely encosed by three

or more straight edges.


https://www.youtube.com/watch?v=IaoZhhx_I9s&index=4&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n

TRIANGLES

A triangle is any three-side shape. It is a shape

formed when three non-collinear points are

connected by segments.


TRIANGLES CLASSIFIED BY THEIR ANGLES

All of the angles are

acute (less than 90º)

One of the angles is 90º

One of the angles is

obtuse (more than 90º)


TRIANGLES CLASSIFIED BY THEIR SIDES

None of their sides or

angles are equal

All three sides ares the

same length. All three

angles are 60º

Two of the sides are the same length.

Two of the angles are equal.


IMPORTANT LINES AND POINT IN A TRIANGLE

A median of a triangle is a segment from a vertex

to the midpoint of the opposite side of the vertex. The

baricentre or centroid is the point at which the three

medians intersect.


IMPORTANT LINES AND POINT IN A TRIANGLE

An altitude is a segment of a perpendicular straight

line to a side of the triangle or its prolongation, traced

for the opposing vertex.

The orthocentre is the point at which the three

(possibly extended) altitudes of a triangle intersect.


QUADRILATERALS

A quadrilateral is any four-side shape.

The two diagonals of a quadrilateral go from one

corner to the opposite corner.


QUADRILATERALS. PARALLELOGRAMS

Parallelograms are quadrilaterals which opposite sides

are parallel and are the same length. The diagonals

bisect each other, i.e. they cut each other in its

midpoint.

There are four types of parallelograms: squares,

rectangles, rhombuses, and Romboids.


SQUARE

All sides are the same length.

All angles are 90º.

Diagonals are perpendicular.

It has 4 lines of symmetry.


RECTANGLE

Opposite sides are the same length.

All angles are 90º.



RHOMBUS

All sides are the same length.

Opposite angles are equal.

Diagonals are perpendicular.



RHOMBOID

No right angles

It has adjacent sides of different length.

It has no lines of symmetry.


NON- PARALLELOGRAMS

Trapezium: One pair of opposite sides are parallel.

o Right trapezium: It is a trapezium with two right

angles.

o Isosceles Trapezium: It is a trapezium with two non–

parallel sides of the same length. It has one line of

symmetry.


NON- PARALLELOGRAMS

Trapezoid: A trapezoid is a quadrilateral with no

parallel sides.

* Kite:

* A quadrilateral is called concave if one of its diagonals is outside:


REGULAR POLYGONS

A regular polygon has all its sides of the same length

and all its angles are the same.

All regular polygons have as many lines of symmetry as

they have sides


REGULAR POLYGONS

The centre (O) is the point inside that is equidistant from each

vertex.

The radious (r) is the distance from the centre to any vertex.

The apothem (a) is a line drawn from the centre to the

midpoint of one side.


PYTHAGORAS’ THEOREM

In a right triangle, its hypotenuse is the side opposite

of the right angle. The other two sides are called legs.

The Pythagoras’ theorem says that in a right

triangle, the square of the length of the hypotenuse a

is equal to the sum of the squares of the other two

sides, b and c.2 2 2a b c



Moreover,

Find out what type of triangle is if its sides are 6, 5, 7

cm.

2 2 2

2 2 2

2 2 2

The triangle is a

The triangle is

right triangle

acute triangle

obtu

an

The se tritriang ale is an n gle

a b c

a b c

a b c


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GEOMETRICAL SHAPES - WordPress.com€¦ · PYTHAGORAS’ THEOREM In a right triangle, its hypotenuse is the side opposite of the right angle. The other two sides are called legs