Pythagoras and Triangles

  Names of shapes of the different triangles

There are 7 types of triangles:  

• Equilateral

• right isosceles

• obtuse isosceles

• acute isosceles

• right scalene

• obtuse

• acute

Equilateral- In geometry, an equilateral triangle is a triangle whose all three sides are of equal length.

Obtuse Scalene- An obtuse triangle is any triangle that has an obtuse angle. An obtuse angle is one that measures greater than 90 degrees. An acute angle is one that measures less than 90 degrees. A scalene triangle is one that has all three sides of a triangle of different lengths and all three angles of different measures.

Acute Scalene- As mentioned, an acute triangle consists of three acute angles (measuring less than 90 degrees), while scalene triangles contain three unequal sides and angles. Therefore, an acute scalene triangle has the following properties: Three intersecting line segments. Three acute angles. None of the sides are equal.

Obtuse isosceles - An isosceles triangle is a triangle that has at least two equal sides. So, for an isosceles triangle to be considered obtuse, it just has to be a triangle with two equal sides and an angle that is between 90 degrees and 180 degrees.

Acute Isosceles - Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

Right scalene - It has no equal sides so it is a scalene right-angled triangle. And, like all triangles, the three angles always add up to 180°

Who is Pythagoras?

Pythagoras was a Greek philosopher and mathematician. 

What did he do?

As part of his education, when he was about age 20 he apparently visited the philosophers Thales and Anaximander on the island of Miletus.

Pythagoras Theorem

The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle.

What are Square and Square Root?

In math, squares and square roots are inverse operations. The Square of a number is the value of power 2 of the number, while the square root of a number is the number that we need to multiply by itself to get the original number

Cos. In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Tan. in a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. The tangent function, along with sine and cosine, is one of the three most common trigonometric functions.

Link to work out Sin Cos Tan

Trigonometry Angles

Trigonometry angles are the angles given by the ratios of the trigonometric functions. Trigonometry deals with the study of the relationship between angles and the sides of a triangle. The angle value ranges from 0-360 degrees. The important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°.

Square: Squaring in when you times a number by itself. For example, 8 x 8 = 82

Square Root: a number that produces a specified quantity when multiplied by itself.  

Square root symbol> √

This is a photo of Pythagoras.

Connections- Klara and the Sun and Blade Runner 2049

Connections between Klara and the Sun and Blade Runner 2049?

Discrimination:

• Blade Runner- Replicants get discriminated because they aren't fully human. The non- replicants are shown as royalty because they are fully human and they somehow feel like their better than everyone.

• Klara and the Sun- The people who are lifted are discriminated against because they are shown as a disgrace to the human population. The people who haven't been lifted are shown as normal people.

What is love:

• Klara and the Sun- In this book, we see that Klara says "Love isn't what you feel on the inside, it's what everyone else's feels about you".

• Blade Runner- Even though Joi isn't a real person, K still loves her for who she is, he doesn't care if she's real or not.

How to Label a Triangle

When labeling a triangle, there are a couple of rules around it. 

• When labeling a triangle, all of the angles on the triangle must be a capital letter. 
• All sides of a triangle must be labeled with a lower case letter.
• Each letter must be opposite from the other. For example- Angle A should be opposite of side a, same with angle B and angle C.

You do not use this rule with a RAT (right angle triangle) because you only have one of each letter on those triangles.