Construct a triangle such that AB=3cm,AC=4cm,BAC=90° verify the truth of Pythagoras theorem in your own words
Answers
Answer:
ASSUMED KNOWLEDGE
Familiarity with measurement of lengths, angles and area.
Basic knowledge of congruence and similarity.
Familiarity with simple geometric proofs.
Simple geometric constructions.
Factorisation of whole numbers.
Simple surd notation.
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MOTIVATION
Is there a simple relationship between the length of the sides of a triangle? Apart from the fact that the sum of any two sides is greater than the third, there is, in general, no simple relationship between the three sides of a triangle.
Among the set of all triangles, there is a special class, known as right-angled triangles or right triangles that contain a right angle. The longest side in a right-angled triangle is called the hypotenuse. The word is connected with a Greek word meaning to stretch because the ancient Egyptians discovered that if you take a piece of rope, mark off 3 units, then 4 units and then 5 units, this can be stretched to form a triangle that contains a right angle. This was very useful to the Egyptian builders.
This raises all sorts of questions. What is so special about the lengths 3, 4 and 5? Are there other sets of numbers with this property? Is there a simple relationship between the lengths of the sides in a right-angled triangle? Given the lengths of the sides of a triangle, can we tell whether or not the triangle is right angled?
Most adults remember the mathematical formula
c2 = a2 + b2