How do I know if triangle ABC contains a right angle? (where AB=10cm, BC= 8cm, CA= 6cm)
When using Pythagoras' theorem, the hypotenuse squared should equal the square of the other two sides added together, so (a2=b2+c2). We also know that for Pythagoras' theorem to work, one of the angles must be a right angle (90 degrees) and the other two should be acute angles (less than 90 degrees). To prove that the triangle ABC contains a right angle, we need to show that Pythagoras' theorem works for this triangle where AB=10cm, BC=8cm and CA=6cm, so prove that AB2=BC2+CA2 where the hypotenuse is AB=10 and the other two sides are BC=8 and CA=6. To do this, substitute the numbers into the equation, giving us 102=82+62. The next step is proving that this equation does, in fact, work, so we should prove that the right hand side equals the left hand side. If the two sides equal each other this triangle is a right angle triangle and can therefore be used for Pythagoras' theorem. So the left hand side equals 100cm and the right hand side equals 64+36=100cm, therefore (left hand side)=(right hand side) and (100=100), proving that the triangle contains a right angle as required.
