Mathematics Grade 9: Calculating angles (Inc. Pythagoras)

Introduction

Good day Grade 9's.

I welcome you to a new section in our mathematics curriculum.

In this chapter we will be focusing on shapes and calculating interior angle, exterior angels, corresponding angles, co-interior angles,

angles on a straight line etc.

This will give you the opportunity to become familiar with different angles and what they entail. use the link below to watch a video on some examples and calculations based on angles.

 

Task

Definition of pythagoras.

in mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ab and c, often called the Pythagorean equation:[1]

{\displaystyle a^{2}+b^{2}=c^{2},}a^{2}+b^{2}=c^{2},

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. The theorem, whose history is the subject of much debate, is named for the Greek thinker Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods—possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

Calculating angles (formula's)

Interior angles: Interior angles add up to 180 Degrees

Exterior angles: Interior angles add up 180 Degrees

Supplementary angles: Add up to 180 Degrees

Formula for calculating the theorem of pythagoras: A(Squared) + B(Squared) = C(Squared)

 

Process

Activity 1

Given the information provided in the task section, calculate and answer the follow questions.

  1. provide the formula for calculating the theorem of pythagoras in words.
  2. If the value of a = 4 (Squared) and b = 5 (Squared), calculate c.
  3. Interior angles of a triangle add up to?
  4. Angles on a straight line add up to?

 

Evaluation

Answers to Activity 1

1. In a right angle triangle, the hypotenuse is equal to the sum of the other two sides squared.

2. 4 squared = 16

    5 squared = 25

    6 + 25 = 41

    C = 41 Squared

    C = 6,4 

3. Interior angles on a triangle add up to 180 Degrees.

4. Angles on a Straight line add up to 180 Degrees.

Marking grid
Q1 2 marks
Q2 4 marks
Q3 2 marks
Q4  2 marks

Total Marks : 10 Marks

Conclusion

Well Done !!

As we come to the end of our first session based on Angles of a triangle, I want to thank all who participated in this lesson which serves as a stepping stone as to what we will be engaging in on a later stage when we go into more in depth angles.

Based on what you learned in this stepping stone to angles of a triangle, use the link below to get a taste of what is yet to come in future, we will take it one step at a time to ensure no one will be left behind. #TeamWorkMakesTheDreamWork!!!

218096844

Ronel Fortuin

218096844fortuin@gmail.com

 

Credits