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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn about the contributions Thales and Pythagoras made to the study of geometry. Also learn which of their major contributions is still in use today.

Geometry is about shapes. It is about defining the characteristics of different shapes. It is about drawing shapes and being able to calculate their dimensions, areas, and volumes. Today, we have formulas that have been proven to work time and time again over the centuries. We have systems in place that help us to visualize and work out problems. But how did they come about? It is all thanks to people like Thales and Pythagoras that we are where we are today in the field of geometry. This video lesson is all about the contributions Thales and Pythagoras made to the study of geometry. Watch and see which one of their teachings you use the most.

Thales comes from Miletus in Asia Minor and was a Greek. He was born around 624 BC and died around 547 BC. Yes, that was a long time ago, but he made some very major contributions to the field of geometry. In fact, some consider him the first mathematician. On a visit to Egypt, he was able to calculate the height of a pyramid. He is credited for making five notable contributions to the field of geometry, one of which is named after him.

The first is that the diameter of a circle bisects, or cuts, the circle in half. The second is that the base angles of an isosceles triangle are equal to each other. The third is when you have two straight lines intersecting each other, the opposite or vertical angles are equal to each other. The fourth notable contribution states that when two triangles have two equal angles and one equal side, then they are congruent, or equal, to each other. The fifth is called Thales' Theorem. It states that an angle that is inscribed or drawn inside a half-circle or semicircle will be a right angle. These five contributions are credited to Thales because he provided the first written proof of these theorems. Now, let's talk about Pythagoras.

Pythagoras was born around 569 BC in Greece and lived to sometime around 500 - 475 BC. While Thales was referred to as the first mathematician, Pythagoras was called the first pure mathematician. No wonder, since Thales had actually given Pythagoras advice on how he could advance his mathematical knowledge. Pythagoras also made major contributions to the study of geometry and he is given credit for the following four teachings.

The first is that the three angles of a triangle will add up to two right angles or 180 degrees. The second is named after him. It is called the Pythagorean Theorem, which tells us that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. The third is the use and construction of various figures and shapes to solve equations. The fourth is that Pythagoras understood and was able to construct a tetrahedron, a cube, and an octahedron. Pythagoras is credited with these teachings because he, like Thales, provided the first written proof of these.

We've talked about both Thales and Pythagoras now. Which one of their teachings do you use most often? You might say it is the Pythagorean Theorem, and if you go further in depth, you might say it is Thales' Theorem. Or it might be their other contributions. Whichever you choose, you can see that all of their contributions are still in use today and mathematicians of today sometimes use their teachings to prove even more theorems.

What have we learned? We've learned that both Thales and Pythagoras are Greek. Their life spans overlapped each other and Thales actually advised Pythagoras in his mathematical quest for more knowledge. Both contributed much to the study of geometry. Thales is credited for teaching that a diameter bisects a circle, the base angles of an isosceles triangle are equal, the opposite or vertical angles of two intersecting straight lines are equal, two triangles are equal if they have two angles and one line that are the same, and that an angle drawn inside a semicircle will be a right angle. This last teaching is also known as Thales' Theorem.

Pythagoras is credited for teaching that the angles of a triangle will add up to 180 degrees or two right angles; the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides; the construction of figures and shapes can be used to solve equations; and the construction of a tetrahedron, cube, and octahedron.

After you've completed this lesson, you should be able to:

- Summarize both Thales' and Pythagoras' backgrounds
- Explain the mathematical concepts that each are credited with establishing

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Geometry: High School15 chapters | 160 lessons

- What is Geometry? 4:36
- Inductive & Deductive Reasoning in Geometry: Definition & Uses 4:59
- Thales & Pythagoras: Early Contributions to Geometry 5:14
- Euclid's Axiomatic Geometry: Developments & Postulates 5:58
- Undefined Terms of Geometry: Concepts & Significance 5:23
- Properties and Postulates of Geometric Figures 4:53
- Algebraic Laws and Geometric Postulates 5:37
- Go to High School Geometry: Foundations of Geometry

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