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3.3 If you only receive the information as in the sketches below, can you say with certainty that the two triangles are a lw a ys congruent?

DEFρCBAρ3.4 Will the following two triangles be congruent? Why?

4.1 Study page A-4 of the accurately constructed triangles. All the triangles on page A-4 were constructed by using two sides and the angle not between the two given sides, (ss ) Study these triangles and write down the pairs of triangles which are congruent. Again remember to write down the triangles in order of the elements which are equal.

4.2 There are two triangles, which, although the two sides and the angle are equal, are not congruent. Name them.

4.3.1 Do you think that, if two sides and the angle not between the two sides, are used to construct triangles they would always be congruent?

4.3.2 What condition must the given sides satisfy for the triangles to be congruent?

4.4.4 If you only receive the information as in the sketches below, can you with certainty say that the two triangles are always congruent? (Remember you now do not know what the lengths of the two given sides).

4.5.1 There are four triangles on page A-4 where the given angle is 90°. If the angle not between the two given sides is equal to 90°, do you think that the two triangles will always be congruent? (rhs)

4.5.2 If you only receive the information like in the two sketches below, can you with certainty say that the two triangles are always be congruent?

5. On page A-5 there are triangles of which the three angles of the one triangle are equal to the three angles of the other triangle. (  )

5.1 Are the triangles constructed like this always necessarily congruent?

5.2 If you only receive the information like in the two sketches below, can you with certainty say that the two triangles are always be congruent?

6. Now give the combinations of sides and angles for triangles to be congruent. Illustrate each combination as in the e x ample below:

1.

Homework assignment

1. State whether the following pairs of triangles are congruent or not. Do each number like the example below.

Example:

 A =  D; B = E and C = F

N.B. If the triangles are not necessarily congruent, only write ΔABC  ΔDEF and then write down why you say so.

  • The triangles are not drawn to scale. You must only use the given information in each of the figures.

2. In each of the following pairs of triangles two pairs of equal elements are marked. In each case write down another pair of equal elements for the triangles to be congruent. Give the congruency test which you used and also give all the possibilities without repeating a congruency test.

Assessment

LO 3
Space and Shape (Geometry)The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.
We know this when the learner :
3.1 recognises, visualises and names geometric figures and solids in natural and cultural forms and geometric settings, including:3.1.1 regular and irregular polygons and polyhedra;3.1.2 spheres;3.1.3 cylinders;3.2 in contexts that include those that may be used to build awareness of social, cultural and environmental issues, describes the interrelationships of the properties of geometric figures and solids with justification, including:3.2.1 congruence and straight line geometry;3.3 uses geometry of straight lines and triangles to solve problems and to justify relationships in geometric figures;3.4 draws and/or constructs geometric figures and makes models of solids in order to investigate and compare their properties and model situations in the environment;
3.5 uses transformations, congruence and similarity to investigate, describe and justify (alone and/or as a member of a group or team) properties of geometric figures and solids, including tests for similarity and congruence of triangles.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
Berger describes sociologists as concerned with
Mueller Reply
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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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