Tnagled with Right Triangles - padlet.com/kirti902/edtech by kirti tripathi

2015-03-02 06:20:35 UTC

Group 1- Oorvi Gupta

2015-10-05 08:01:34 UTC

area of a hexagon= 6* area of a equilateral triangle = 6* sqrt(3) *sqr(a)/4

after solving alegebrcally We saw that a regular hexagon fits the Pythagoras theorem.

Group-2-Sonakshi Gupta

2015-10-05 08:07:53 UTC

Area of an equilateral triangle is square root of 3 divided by 4 multiplied by square of the side.

We saw that a equilateral triangle fits the Pythagoras theorem.

Group -3 Uday

kirti902 — 2015-10-05 08:46:13 UTC

We had taken a irregular figure rectangle. we took width constant for all the 3 rectangle ,calculated area and found that Pythagoras theorem does not hold true

Later with the help of my teacher I took width in proportion of length ie width was half of length and found that It became true so my finding is in a irregular figure like rectangle if we take sides in proportion ie for similar figures theorem holds true

Group

kirti902 — 2015-10-05 08:50:11 UTC

We took circles and semicircles to explore that if we take a circle with radius equal to 3 sides of right triangle the area happens to be the same .

Repeated same thing by taking diameter as 3 sides of right triangle still the Pythagoras theorem is true

Same thing repeated with semicircles and still the theorem holds true

Group 5

kirti902 — 2015-10-05 08:53:24 UTC

We worked with regular pentagons

Used paper folding to convert it into 5 equal triangles , calculated altitude and found out area of one and pentagon area was equal to 5 * area of triangle

We found that the area of pentagon at side C is equal to area at side A and area at side B

Group 6

kirti902 — 2015-10-05 08:57:04 UTC

We took an isosceles triangle and made isosceles triangles at all 3 sides considering their altitude same as base . After calculation found that it satisfies the Pythagoras theorem .

Later after discussing in my group we found that if take altitude which not in proportion with base the theorem does not hold true.

So we concluded that in case of isosceles triangles if base & altitude ratio is maintained in all 3 triangle the theorem hold s true

Class observation

kirti902 — 2015-10-05 09:02:11 UTC

The class together found a relation ship between triplets that if X,Y Z are triplets then any multiples of these will also be Pythagoras triplet

ie nX, nY and nZ will also be triplets

Kirti Teacher

kirti902 — 2015-10-05 09:03:46 UTC

All groups have seen that when area is being calculated using any figure , it has a square term multiplied by a unique factor

so if A,B ,C are pythogorus triplet

then

Sqr(A) +Sqr(B) = Sqr(C)

and also

F* Sqr(A) +F*Sqr(B) = F* Sqr(C)

will also be true

So for regular figures pythagoras theorem holds true

Kirti Teacher

kirti902 — 2015-10-05 09:10:07 UTC

In case irregular figure the common finding was that area of the figure fullfils Pythagoras theorem only if the figures follow similarity concept ie like in rectangle when length and width are take in proportion of 1/2 it satisfied the theorem

Similarly consider the case of isosceles triangle , theorem satisfies when we take base and altitude in proportion

So if figures are similar them also theorem hold true

Class Observation

kirti902 — 2015-10-05 09:14:47 UTC

All Figures had area formula containing square of the side multiplied by some area factor

Hence the theorem was evaluated to true for all regular polygons

Area of Polygon( Side C) =Area of polygon(Side B) + Area of polygon (Side C)

Factor * Sqr(C) = Factor * Sqr(A) + Factor * Sqr(A) +Factor * Sqr(B)

Class Observation

kirti902 — 2015-10-05 09:21:43 UTC

In case of irregular shape if same proportion is maintained

then above equation remains true so -

Factor * Sqr(C) = Factor * Sqr(A) + Factor * Sqr(A) +Factor * Sqr(B)

Since we have maintained same proportion we say that figures are similar