Similarity and Trigonometry (Triangles)

TrianglesBasic Proportionality Theroem

Areas of similar triangles

Trignometry

Basic Proportionality

Theorem

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

Proving the statement right. .

Given : ABC

To prove : AP = AQ PB QC

Construction : PM QC

A

B C

P Q

M

A real life application

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

which deals with ratios, just like the basic proportionality

theorem.

Situation 1

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

Situation 2 Compare the given two squares

Areas Of SimilarTriangles

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

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.

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

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.

Trignometry

• 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”.

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.

The ratios.

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

Real life applications

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

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

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