Colegio Herma. Maths Bilingual Department Isabel Martos Martínez. 2015

1. PYTHAGOREAN THEOREM

In a right triangle one of the angles of the triangle measures

90.

The side opposite the right angle is called the hypotenuse.

The two sides that form the right angle are called the legs.

http://www.mathsisfun.com/pythagoras.html

In a right angled triangle:

The square of the hypotenuse is equal to the sum of the

squares of the other two sides.

It enables us to calculate one side of a right-angled when the

other two sides are known. For example, if the hypothenuse

and one other side are known, the remaining leg can be

calculated by:

Applying Pithagorean Theorem:

1. The height of an equilateral triangle or isosceles.

2. The diagonal of a rectangle

In a triangle where sides are known and a is the longest one:

If the triangle is right-angled it is true that:

a2 = b2 + c2

If the triangle is acute-angled it is true that:

a2 < b2 + c2

If the triangle is obtuse-angled it is true that:

a2 > b2 + c2

2. AREA OF PLANE (TWO DIMENSIONAL) SHAPES

Rectangle: A = base · height = b · h

Square: A = side · side = l2

Paralelogram: A = base · height = b · h

Rhombus:

Trapecium: h

b

Triangles: h

b

Circles: A = pi · squared radius = π·r2 r

Regular Polygons: a

Area of special shapes

CIRCLE CIRCLE SECTOR

A = π·r2 A = π·r2 · 𝛼

360

ANNULUS ELLIPSE

A = π (R2 – r2 ) A = π ·a ·b

In the following videos you will see the “Special properties and parts of a triangles”

In the first one you will see this topic in English. In the others you will see it in Spanish. The second video shows you the concepts and definitions, and in the last one you will learn how to draw:

• Perpendicular bisector and Circumcenter (mediatrices y circuncentro)

• Angle bisector and Inradio (bisectrices e incentro)

• Medians and Centroid (medianas y baricentro)

• Altitudes and Orthocenter (alturas y ortocentro)

Special properties and parts of a triangle

Conceptos y definiciones de rectas y puntos notables de un triángulo

Cómo trazar las rectas y puntos notables de un triángulo