# 2.2 Classifying and constructing triangles

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## [lo 3.1, 3.3, 3.4, 4.2.1]

• By the end of this learning unit, you will be able to do the following:
• understand how important the use of triangles is in everyday situations;
• explain how to find the unknown sides of a right-angled triangle (Pythagoras);
• calculate the area of a triangle;
• enjoy the action in geometry;
• use mathematical language to convey mathematical ideas, concepts, generalisations and mental processes.

1. When you classify triangles you can do it according to the angles or according to the sides.

1.1 Classification on the basis of the angles of a triangle:Are you able to complete the following?

a) Acute-angled triangles are triangles with

b) Right-angled triangles have

c) Obtuse-angled triangles have

1.2 Classification on the basis of the sides of the triangle:Are you able to complete the following?

a) An isosceles triangle has

b) An equilateral triangle has

c) A scalene triangle's

2. Are you able to complete the following theorems about triangles? Use a sketch to illustrate each of the theorems graphically.

THEOREM 1:

• The sum of the interior angles of any triangle is.........................

Sketch:

THEOREM 2:

• The exterior angle of a triangle is

Sketch:

3. Constructing triangles:

• Equipment: compasses, protractor, pencil and ruler

Remember this:

• Begin by drawing a rough sketch of the possible appearance.
• Begin by drawing the base line.

3.1 Construct $\Delta$ PQR with PQ = 7 cm, PR = 5 cm and $\stackrel{ˆ}{P}$ = 70°.

a) Sketch:

b) Measure the following:

1. QR = ........ 2. $\stackrel{ˆ}{R}$ = ........ 3. $\stackrel{ˆ}{Q}$ = ........ 4. $\stackrel{ˆ}{P}+\stackrel{ˆ}{Q}+\stackrel{ˆ}{R}=$ ........

3.2 Construct $\Delta$ KLM , an equilateral triangle. KM = 40 mm, KL = LM and $\stackrel{ˆ}{K}$ = 75°.Indicate the sizes of all the angles in your sketch.

Sketch:

## [lo 4.2.1, 4.8, 4.9, 4.10]

• The following could be done in groups.

Practical exercise: Making you own tangram.

1. Cut out a cardboard square (10 cm x 10 cm).

2. Draw both diagonals, because they form part of the bases of some figures.

3. Divide the square in such a way that the complete figure consists of the following:

3.1 two large equilateral triangles with bases of 10 cm in length;

3.2 two smaller equilateral triangles, each with base 5 cm in length;

3.3 one medium equilateral triangle with adjacent sides 5 cm in length;

3.4 one square with diagonals of 5cm;

3.5 one parallelogram with opposite sides of 5 cm.

• Make two of these. Cut along all the lines so that you will have two sets of the above shapes.

4. Now trace the largest triangle of your tangram in your workbook as a right-angled triangle.

5. Arrange the seven pieces to form a square and place this on the hypotenuse of the traced triangle.

6. Now arrange the two largest triangles to form a square and place this on one of the sides adja­cent to the right angle of the traced triangle.

7. Arrange the remaining pieces to form a square and place this on the other adjacent side.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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Sherica
im all ears I need to learn
Sherica
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Tamia
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Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
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Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
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Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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