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Pythagoras: The Converse SACHS
Contributed by: Shanahan
normally, used in a right angled triangleto calculate the value of a missing side
converse, use the three sides to
see if the triangle is right angled
Converse is used when the elements       of a proposition are reversed.
Hit - OK below
We know this, because c is the hypotenuse (longest side).
e.g.1. A triangle has sides 8cm, 11cm and 5cm.
          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
c2 = a2 + b2
2
= 52 +
2
e.g.1. A triangle has sides 8cm, 11cm and 5cm.
          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
Calculator:
112 = 52 + 82
c2 = a2 + b2
 =
(52 + 82 =)
e.g.1. A triangle has sides 8cm, 11cm and 5cm.
          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
Incorrect statement, the triangle is not right angled.
Correct statement, the triangle is right angled.
121 = 89
112 = 52 + 82
c2 = a2 + b2
We know this, because c is the hypotenuse (longest side).
e.g.2. A triangle has sides 12cm, 20cm and 16cm.          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
c2 = a2 + b2
2
= 122 +
2
e.g.2. A triangle has sides 12cm, 20cm and 16cm.          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
Calculator:
202 = 122 + 162
c2 = a2 + b2
 =
Incorrect statement, the triangle is not right angled.
Correct statement, the triangle is right angled.
e.g.2. A triangle has sides 12cm, 20cm and 16cm.          Is it right angled?
If the triangle is right angled, then c2 = a2 + b2.
400 = 400
202 = 122 + 162
c2 = a2 + b2
We know this, because c is the hypotenuse (longest side).
If the values form a Pythagorean triad, then c2 = a2 + b2.
e.g.3. Is 8, 15 and 17 a Pythagorean triad?
c2 = a2 + b2
2
= 82 +
2
If the values form a Pythagorean triad, then c2 = a2 + b2.
Calculator:
e.g.3. Is 8, 15 and 17 a Pythagorean triad?
172 = 82 + 152
c2 = a2 + b2
=
If the values form a Pythagorean triad, then c2 = a2 + b2.
Incorrect statement, it is not a Pythagorean triad.
Correct statement, it is a Pythagorean triad.
e.g.3. Is 8, 15 and 17 a Pythagorean triad?
289 = 289
172 = 82 + 152
c2 = a2 + b2
A triad (or triple) is Pythagorean, if the 3 valuesform a correct statement when substitutedinto c2 = a2 + b2.
A triangle is right angled if the 3 side lengthsform a correct statement when substitutedinto c2 = a2 + b2.
The converse of Pythagoras' Theorem
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