Converse of Pythagoras theoremIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

State the converse of Pythagoras' theorem.
Where is the right angle in a triangle that passes the test?
What are the steps to test for a right angle?
When is a triangle acute-angled?
When is a triangle obtuse-angled?
What is a Pythagorean triple?
Name two Pythagorean triples apart from 3,4,5.
How can you make more Pythagorean triples from one?
What is an equilateral triangle?
What is an isosceles triangle?
What is a scalene triangle?
What condition must the sides satisfy to form a triangle?
Why can a rounded measurement make a right-angle test unreliable?

Exam questions on Converse of Pythagoras theorem

A triangle has sides of length $9$ cm, $12$ cm and $15$ cm.
Find the area of the triangle.2 marks
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).