Currently viewing the tag: "Theorem of Pythagoras"
Investigating proofs of Pythagoras Theorem by similar triangles and practical jig-saw methods. Extension to the Cosine Rule.
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Draw a triangle with angles x, (45 + x) and (45 – x) degrees.
What does Pythagoras Theorem tell you about these angles?
Use this information to find this sum of squares of sines:
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What is the area, (in square units) of the triangle formed by the three lines whose equations are: y − x = 6, x − 2y = 3 and x + y = 6?
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1. Find the area of the quadrilateral.
2. The rectangle is cut into two pieces along the dotted line and rearranged to make a triangle. Find the perimeter of the triangle.
The diagram shows a septagon ABCDEFG in which the lengths GA, AB, BC, CD, DE, EF are all equal and FG = 6 units. The area of the square BDFG is half the area of the septagon. Find the perimeter of the septagon.
This rectangle measures three units by one unit.
The diagram shows three angles a, b and c.
How many ways can you prove that a + b = c?
What other interesting properties can you find?
When this activity was originally published on NRICH, two boys from Madras School in St Andrew’s, Scotland sent […]
Seven squares are drawn inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.
The centre square has the area of 1 (one) square unit.
Draw the diagram. You can download square dotty paper here.
What is […]
This is a unit circle with a tangent at A.
The angle marked in the diagram is angle a.
Copy the diagram and find all the angles in terms of the angle a.
Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.
Find the areas of […]
Imagine you have a pencil, ruler, protractor and compass and you try to draw this triangle. Is it possible?
If you have geometry instruments then try it for yourself. What do you notice?
Can you give reasons for your answer to the question “Is it possible?”
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