Converse of Pythagoras theoremIB MYP Maths Extended: Mind map

Exam questions on Converse of Pythagoras theorem

1. A triangle has sides of length $9$ cm, $12$ cm and $15$ cm.
   Find the area of the triangle.2 marks
2. Carpenters check that the corner of a rectangular frame is square by measuring the two sides at the corner and the diagonal opposite it. For one frame the sides are $2.4$ m and $1.8$ m, and the diagonal is measured as $3.1$ m.
   The carpenter adjusts the frame until the diagonal measures exactly $3.0$ m. Explain, with a calculation, why the corner is now a right angle.2 marks
3. Aisha investigates whole-number triples $(a,b,c)$ that satisfy $a^2+b^2=c^2$, called Pythagorean triples. She finds $(3,4,5)$, $(6,8,10)$ and $(9,12,15)$.
   Describe the pattern in the three triples and write a general rule for further triples. Verify your rule using the next triple in the pattern.3 marks