GRADE 8

LESSON FOR CLASSMATES 20 January 2016, by Natálie Vnenková

„Pythagorean theorem“

This project was funded by European Union.

„Teaching: An effective key to self-learning“for project:

HELLO! I AM NATALI AND I PREPARED THIS LESSON FOR MY CLASSMATES FROM 8. A

LET´S START - THE BEGINNING

The Pythagorean theorem was named after Pythagoras form Sam. He was the first person who proved it. This theorem was probably known also in China, Egypt and before the Ancient Greece.

FORMULA: DEFINITION: It states that the square of the hypotenuse

(the side opposite the right angle) is equal to the sum of the squares of the other two sides.

c2 = a2+ b2

CLIL – LISTEN, REPEAT

MY PROBLEMS FOR INDIVIDUAL WORK 1) Try to calculate whether a triangle with sides 1.5 cm, 2 cm and 2.5cm long is right-angled. 2) What is the area of a triangle if one side is 3.5 cm long and the diagonal measures 9.1 cm?

QUIZ – CHECKING UNDERSTANDING1) For which triangle applies the Pythagorean theorem?a) Any triangle b) An equilateral triangle c) A

right triangle 2) If „c“ is the hypotenuse and legs are „a“ and „b“,

which equations stands for the Pythagorean theorem?

a) c2 = a2 + b2 b) c = a + b c) c2 = a2 - b2

ANSWERS FOR INDIVIDUAL WORK:

1) Yes, it is a right triangle.

2) S = 29.4 cm2Test: 1c, 2a

EXPLANATION OF THE RESULT:

WE WILL USE THE PYTHAGOREAN THEOREM - FORMULA FOR THE LEG:

DANIEL CALCULATED THE ROOT:

THEN HE CALCULATED THE AREA

REVISION – PROOFWe saw this proof in the Science Museum in Ostrava which we visited in January 2015 with our international partners during the 1st project meeting. There is a red liquid in the squares and you can turn the wheel with the squares.

SCIENCE MUSEUM IN OSTRAVA