<< Chapter < Page Chapter >> Page >

We use the symbol ||| to mean is similar to .

Similar Polygons

Two polygons are similar if:

  1. their corresponding angles are equal, and
  2. the ratios of corresponding sides are equal.

Show that the following two polygons are similar.

  1. We are required to show that the pair of polygons is similar. We can do this by showing that the ratio of corresponding sides is equal and by showing that corresponding angles are equal.

  2. We are given the angles. So, we can show that corresponding angles are equal.

  3. All angles are given to be 90 and

    A ^ = E ^ B ^ = F ^ C ^ = G ^ D ^ = H ^
  4. We first need to see which sides correspond. The rectangles have two equal long sides and two equal short sides. We need to compare the ratio of the long side lengths of the two different rectangles as well as the ratio of the short side lenghts.

    Long sides, large rectangle values over small rectangle values:

    Ratio = 2 L L = 2

    Short sides, large rectangle values over small rectangle values:

    Ratio = L 1 2 L = 1 1 2 = 2

    The ratios of the corresponding sides are equal, 2 in this case.

  5. Since corresponding angles are equal and the ratios of the corresponding sides are equal the polygons ABCD and EFGH are similar.

Got questions? Get instant answers now!
All squares are similar.

If two pentagons ABCDE and GHJKL are similar, determine the lengths of the sides and angles labelled with letters:

  1. We are given that ABCDE and GHJKL are similar. This means that:

    AB GH = BC HJ = CD JK = DE KL = EA LG

    and

    A ^ = G ^ B ^ = H ^ C ^ = J ^ D ^ = K ^ E ^ = L ^
  2. We are required to determine the

    1. a , b , c and d , and
    2. e , f and g .
  3. The corresponding angles are equal, so no calculation is needed. We are given one pair of sides D C and K J that correspond. D C K J = 4 , 5 3 = 1 , 5 so we know that all sides of K J H G L are 1,5 times smaller than A B C D E .

  4. a 2 = 1 , 5 a = 2 × 1 , 5 = 3 b 1 , 5 = 1 , 5 b = 1 , 5 × 1 , 5 = 2 , 25 6 c = 1 , 5 c = 6 ÷ 1 , 5 = 4 d = 3 1 , 5 d = 2
  5. e = 92 ( corresponds to H ) f = 120 ( corresponds to D ) g = 40 ( corresponds to E )
  6. a = 3 b = 2 , 25 c = 4 d = 2 e = 92 f = 120 g = 40
Got questions? Get instant answers now!

Activity: similarity of equilateral triangles

Working in pairs, show that all equilateral triangles are similar.

Polygons-mixed

  1. Find the values of the unknowns in each case. Give reasons.
  2. Find the angles and lengths marked with letters in the following figures:

Investigation: defining polygons

Investigate the different ways of defining polygons. Polygons that you should pay special attention to are:

  • Isoceles, equilateral and right-angled triangle
  • Kites, parallelograms, rectangles, rhombuses (or 'rhombi'), squares and trapeziums

Things to consider are how these figures have been defined in this book and what alternative definitions exist. For example, a triangle is a three-sided polygon or a figure having three sides and three angles. Triangles can be classified using either their sides or their angles. Could you also classify quadrilaterals in this way? What other names exist for these figures? For example, quadrilaterals can also be called tetragons.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 maths [caps]' conversation and receive update notifications?

Ask