IB MYP 4-5 Maths- Converse of Pythagoras’ theorem- Study Notes - New Syllabus
IB MYP 4-5 Maths- Converse of Pythagoras’ theorem – Study Notes
Extended
- Converse of Pythagoras’ theorem
IB MYP 4-5 Maths- Converse of Pythagoras’ theorem – Study Notes – All topics
Converse of Pythagoras’ Theorem
Converse of Pythagoras’ Theorem
Statement: If the square of the length of the longest side of a triangle equals the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle.
In Symbolic Form:
If in a triangle with sides \( a, b, c \) (where \( c \) is the longest side), \( c^2 = a^2 + b^2 \), then the triangle is right-angled at the vertex opposite side \( c \).
Steps to Check if a Triangle is Right-Angled:
- Identify the longest side of the triangle.
- Square all three sides.
- Check if (Longest side)² = (Other side)² + (Other side)².
- If true, the triangle is right-angled. Otherwise, it is not.
Example :
Check if a triangle with sides 5 cm, 12 cm, and 13 cm is right-angled.
▶️ Answer/Explanation
Longest side = 13 cm.
Check: \( 13^2 = 169 \).
Other sides: \( 5^2 + 12^2 = 25 + 144 = 169 \).
Since \( 13^2 = 5^2 + 12^2 \), the triangle is right-angled.
Example :
Check if a triangle with sides 7 cm, 24 cm, and 25 cm is right-angled.
▶️ Answer/Explanation
Longest side = 25 cm.
Check: \( 25^2 = 625 \).
Other sides: \( 7^2 + 24^2 = 49 + 576 = 625 \).
Since \( 25^2 = 7^2 + 24^2 \), the triangle is right-angled.
Example :
Check if a triangle with sides 6 cm, 8 cm, and 11 cm is right-angled.
▶️ Answer/Explanation
Longest side = 11 cm.
Check: \( 11^2 = 121 \).
Other sides: \( 6^2 + 8^2 = 36 + 64 = 100 \).
Since \( 121 \neq 100 \), the triangle is not right-angled.
Important Notes:
- Always take the longest side as the possible hypotenuse.
- This test works only for real triangles (triangle inequality must hold).
- If the square of the longest side is greater than the sum of squares of other sides, the triangle is obtuse. If less, it is acute.