similarity and trigonometry (triangles)

21
Triang les Basic Proportiona lity Theroem Areas of similar triangles Trignometr y

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The Basic Proportionality Theorem and the areas of similar traingles proof and the basic trigonometric ratios are explained..

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Page 1: Similarity and Trigonometry (Triangles)

TrianglesBasic Proportionality Theroem

Areas of similar triangles

Trignometry

Page 2: Similarity and Trigonometry (Triangles)

Basic Proportionality

Theorem

Page 3: Similarity and Trigonometry (Triangles)

Statement- If a line is drawn

parallel to one side of a triangle to intersect the other two sides at two distinct points, then the other two sides are divided in the same ratio

Page 4: Similarity and Trigonometry (Triangles)

Proving the statement right. .

Given : ABC

To prove : AP = AQ PB QC

Construction : PM QC

A

B C

P Q

M

Page 5: Similarity and Trigonometry (Triangles)

A real life application

Page 6: Similarity and Trigonometry (Triangles)

Ok, now we’re hopping onto another property of triangles,

which deals with ratios, just like the basic proportionality

theorem.

Page 7: Similarity and Trigonometry (Triangles)

Situation 1

The units of all the above rulers are said to be in centimeters.

Page 8: Similarity and Trigonometry (Triangles)

Situation 2 Compare the given two squares

Page 9: Similarity and Trigonometry (Triangles)

Areas Of SimilarTriangles

Page 10: Similarity and Trigonometry (Triangles)

How do you think the areas of similar triangles would be?

Page 11: Similarity and Trigonometry (Triangles)

A

B C

P

Q R

Theorem - The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Page 12: Similarity and Trigonometry (Triangles)

COULD ANYONE TELL ME HOW COULD SIMILARITY BE USED IN REAL LIFE ?

Page 13: Similarity and Trigonometry (Triangles)

Real life applications of similar triangles• To measure a room’s scale and

size. • Used in light beams to see the

distance from light to the target. • The Wright Brothers used similar

triangles to prepare their landing.

Page 14: Similarity and Trigonometry (Triangles)

Trignometry

Page 15: Similarity and Trigonometry (Triangles)

• Etymology- • The word Trigonometry is derived from

three Greek • words ‘Tries’(three), ‘Goni’(angle/side),

‘Metron’(Measurement).• So, Literally this word means “Measure of

the Triangle”.

Page 16: Similarity and Trigonometry (Triangles)

A right angled triangle has names for each side:•Adjacent is adjacent to the angle "θ",•Opposite is opposite the angle, and•the longest side is the Hypotenuse.

Page 17: Similarity and Trigonometry (Triangles)

The ratios.

Sinθ= opp/HypoCosθ= Adj/HypoTanθ= Opp/AdjCosecθ= Hypo/oppSecθ= Hypo/AdjCotθ= Adj/opp

Page 19: Similarity and Trigonometry (Triangles)

•The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Page 20: Similarity and Trigonometry (Triangles)

•Architects use trigonometry  to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles.

Page 21: Similarity and Trigonometry (Triangles)

There is such a long list if we go further into Triangles..

But it’s time we have to end our presentation.Hope you all liked it.

Presentation by - AnanyaElsaHritikaNisarga