Chapter 13 The Pythagoras’ Theorem
13.1 The Pythagoras’ Theorem
13.1.1 Identify and define the hypotenuse of a right-angled triangle.
Exercise 1: Label the hypotenuse of a right-angled triangle as “h”.
1.
2.
3.
13.1.2 Determine the relationship between the sides of rightangled triangle. Hence, explain the Pythagoras’ Theorem by
referring to the relationship.
Activity 1
One day, Pythagora went to a friend’s house, he saw the tiles on the floor
are in right-angled triangles and seem to have some relation among the three
sides
Problem 1 What is the relation between the three areas of the squares?
________________________
Problem 2 What is the relation in between the sides of right-angled triangle in
between the 3 squares?
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Exercise 2
By using the Pythagoras’ Theorem, find the length of the hypotenuse.
1.
2.
3.
Activity 2
Problem: In any right triangle, is the sum of the squares of the two right-angled
sides equal to the square of the hypotenuse?
1. Teaching aids
: 4 congruent right triangle pieces of paper.
2. Puzzle
: Use 4 right-angled triangle pieces of paper to piece together
a square.
3. Calculate
: the area of the large square.
4. Discovery
: What conclusion?
Method 1:
L: large square
S: small square
R: right-angled triangle
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐿 =
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆 =
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑅 =
𝑀𝑎𝑘𝑒 𝑎 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒𝑠𝑒 𝑡ℎ𝑟𝑒𝑒 𝑎𝑟𝑒𝑎𝑠.
Method 2:
L: large square
S: small square
R: right-angled triangle
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐿 =
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆 =
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑅 =
𝑀𝑎𝑘𝑒 𝑎 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒𝑠𝑒 𝑡ℎ𝑟𝑒𝑒 𝑎𝑟𝑒𝑎𝑠.
Conclusion:
The sum of squares of the two adjacent sides of the triangle is equal to the square
of the hypotenuse.
In other words, ____________________.