# 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.

which of the following is show weak relationship between two variable a/0.27 b/0.80 c/-0.80 d/0.00
is 0.00 show the relationship between two variable weak
Nahom
why not -0.80 ?
Rabia
because -0.80 shows strong negative correlation between the variables
Simran
a/0.27 is correct option d/0.00 means there is no relationship.
King
psychology is the science of brain and behaviour and mind
yes
AB
people think psychology is not science; it is a social science.
yes u r right
AB
Do you have a pdf available for this content?
do you have a pdf of this content?
Ancil
For which?
vidhyalakshmi
stress,coping and wellbeing
Ancil
you can google it, you'll find plenty
Priyank
but i felt contents in this app is awesome , that's why i was looking for the pdf contents of this app
Ancil
Ypp I too feel the content useful
Sakshi
yaaawwwwn
Shawnasie
I could never be a student that would eventually turn me into a college inevevatily into a client and only to ponder what future lifecycles hold
Shawnasie
snap out of it you'll be students for ever for ever ha ha ha ha for ever ha hahaha ha ha
Shawnasie
I'm not going to college. this is just really interesting.
Tori
just for the record Washburn.
Tori
I find it interesting to tori
Shawnasie
what is creative thinking
The thinking process where you are able to project a clutter of ideas and streamline them into concepts that either appeal to or meet the specifications of the target end product of what that thinking process is applied for
Neo
creative thinking could be thinking outside the box, going against the grain sort of speaking.
vincent
Creative thinking is a new way or method in reaching the target which none has used until that particular moment.It is always attractive and easy to reach next levels.And the point is not all people get this sort of thinking.
vidhyalakshmi
What is the difference between drive and motivation?
who would give a psychopath and a sociopath meth amphetamine ( exampels)-louise otero and Sylvia myers
Shawnasie
drive is like a commitment to follow through and motivation is kinda like the desire to follow through.. both together would bring a desire to follow through I suppose
Alexis
Drive is that feeling/reason for the desire to do something, while motivation is that thing which keeps your drive going. Motivation pushes you to achieve what drives you. Drive is the answer for 'how do you do this' while motivation is that catalyst that helps you complete what you started.
Kavya
Why wasn't Carl Jung discussed within the context of historical ( introduction to) psychology?
What are the symptoms of acute stress?
Lose interest in the things that you like to do (for example you like to read or watch movie but when you have acute stress those things don't excite you anymore), feeling tired all day, insomnia / hypersomnia.. and the symptoms has last for quite some time.
Kelly
There are more symptoms but I can't remember it right now
Kelly
Is weight loss one of them ?
Shanice
yeah but you also have to take in consideration as well you may want to think about the full word or question being discussed or asked, starting with the word Acute, so maybe size it levels of stress present are a main focus when answering or giving optional input so yes i agree
Kayla
weight loss or gain it can go both ways ( my personal experience) and it is often hard to break the chain to change back to health level
altug
Okay, thanks.
Shanice
how can we practice personality psychology?
Nasra
what's the captive psychology?
guys you are really mean, you don't even want to at least try to help me. 😢😢😢😢😭😭I thought you were awesome
Nasra
ow
Maxamed
hi Nasra
Ahmet
hi
Mstar
define human emotions and types of emotions
sorry I hit send to many times
vincent
latosha
emotion is a personal conscious experience.
bett
I don't understand sensation and perception 😩
Sensation - detection of basic stimuli (light coming into eyes) Perception - way we interpret the detected stimuli (seeing colours)
Marcel
I second you marcel
Sachin
how can I learn behaviorism
***youtu.be/NNnIGh9g6fA
Any other methods to manage stress ? And Thank You !
Any idea about new ways to manage stress ? And Thank You !
Charbel
I'd like to manage my stress better too how thou?
Shawnasie
a wide array of copping mechanisms that you could alternate between would be my best guess
Shawnasie
I guess, managing stress is not that difficult. When you get some sort of stress, make a pause and leave the place for a while.Get some fresh air,some happy songs,make a convo with your best friend,eat as much as you want,and the best way is to take a nap. :)
vidhyalakshmi
Common symptoms of major depressive disorder include all of the following except......
how many stages do people go through in life and what are their names
Komal
Kathy
anagen , catagen, telogen. or is that just for hair growth only?
Carrie
you should look up Freud and Erikson stages
vincent
Kathy
so much to learn in psych.
Kathy
thank you :)
vincent
Hi
zahir
Guys how are you?
zahir
zahir
I need to understand lot about what
zahir
hi
Tasfia
Abnormal psyh is a huge undertaking...you should take some classes. You could be in school for years, there is so much to learn. I took psych in nursing school and did clinical at a now closed psych institution...and I loved it. The human condition is amazing.
Kathy
Abnormal psych is a great major.
Kathy
Thanks. That's what i need to learn all about behavior. Human beings. Nervous and whats happen in the brain
zahir
I tray to be good for all of those stuff
zahir
Elise
Take intro to psych to see if you enjoy it!
Kathy
Steffenney
Why does anxiety show up alarmingly fast for some people but others show little signs of it?
why does this app have chat
Callum
It is more of a discussion.
Elise
a forum then
Callum
I guess so.
Elise
anxiety stops people from participating so seeing signs of it is usually difficult is it not?
Callum
it's pretty epic
juan
is there an app for psychophysiology?
juan
Not sure what you mean by participating but what I was meaning was anxiety affects others dramatically while some others don't even have anxiety and I was wondering why that occurs.
Elise
by participation i meant anxiety causes fear to move outside your comfort zone or even some activities within it.
Callum
so your question is why do some people have anxiety and some don't?
Callum
I guess so.
Elise
It depends on a person's lifestyle and how the people surrounding them are and the person's mentality
Kevin
I'm not a psychologist I'm an occupational therapists but I'd assume it's a mixture of genetics, environmental factors and development.
Callum
as kevin said
Callum
Right on spot :)
Kevin
It might be because of the natural disposition and personality traits. suppose, if someone is open to new experiences they might not find a new situation challenging enough while on the other hand a person not open to ideas and experience might find himself/herself in a tight corner worrying.
Simran
That is what I thought as well. I have just recently been asked a lot about anxiety and I didnt want to misinforming
Elise
I think it has to do with the way brain is wired for each. some have to build resistance to anxiety whereas others already have a higher resistance to anxiety.
vincent
I struggle with Anxiety very severe. And I don't really know what to do to help get rid of it..
Aryana
anxiety is an elusive but powerful mental problem, it would definitely be intersting to look into it more
Callum
hmmm
Aryana
Anxiety is something that is hard to handle at points. If it gets hard to handle best thing is professional help.
Elise
The best methods i have seen to beat anxiety, i do suffer from it myself, is exposure therapy where you put yourself into those difficult situations like talking to strangers that kind of thing and just working your way through experience
Callum
Well my anxiety is pretty difficult to do that, I get super red when I like get anxiety attacks and other things with it
Aryana
I recommend tai chi or the 1 2 3 breathing exercises
vincent
Also many don't experience anxiety like I do but it will come on randomly and thr best thing to do is breathe.
Elise
yea i can imagine that is why it would have to be in some kind of safe place where you can escape or relax if needed.
Callum
what is tai chi? And yeah I usually do just turn the other way and breathe but still it hits hard
Aryana
there can be multiple reasons behind it. it can also be subjected to sufficient and necessary causes. There can be number of incidents that could have made a person anxious in the past and that has piled up and even similar issue ahead can manifest a lot of reaction and anxiety in future.
Simran
breathing exercises are definitely important too yea
Callum
Yeah thank you
Aryana
Best thing is to just breathe and remember to be relaxed
Elise
if youre not already you should definitely seek seeing someone about it. idk where you guys live but in NZ we get 10 free sessions
Callum
Elise
Yeah, I've been watching to go talk to someone but I can't being myself to get the courage to talk about this
Aryana
There might be an underlying cause behind it and a professional can help you to understand the cause of it and how to break through your inhibitions. You can try out progressive muscle relaxation exercises as well, it will help in calming you down and benefits are way too much there.
Simran
well you can talk here this seems like a reasonably safe place but i would encourage you try to see someone, maybe take a family member, friend for support
Callum
It will be best for physical and emotional health
Elise
Yeah I agree, but sometimes I can't even talk to a family member or friend because I feel like I'm being judged or something but that just comes with the problem
Aryana
i used to feel like that but there is no shame for asking for help and they should support you if want to get better.
Callum
I know how that feels. You will have to accept that you need the help. It may take a while.
Elise
Yeah
Aryana
I honestly wouldn't mind Anxiety if it didn't show in my face and if I didn't have panic attacks
Aryana
well yea the symptoms can be very distressing because as i said before it will stop you from participating in things like social interactions
Callum
Anxiety isn't just caused by social interactions
Elise
Yeah it will, I do online school now because of it..
Aryana
Good day to everyone
Ayomide
ah really, that is very drastic. definitely seek a professional when you can
Callum
good day David
Callum
Thank you
Aryana
It will be hard
Elise
I know its gonna be rough but I'm over it, I'm ready to start living my life again
Aryana
Good thinking
Elise
for sure thats the right attitude Aryana!
Callum
Thank you all very much
Aryana
best of luck
Callum
I think everyone feels Anxiety but degree variates.And when it is out of control person suffers psychologically n physically too.Then symptoms can be observed.To come out or deal with it.One can consult professional help if required or can start with small steps.Like to remember ones strengths etc.
may be because of their living standards and surroundings.If they have already experienced they will not show fast anxiety
Anis
perception..... no?
juan
I think....so
Anis
That is personal belief.
Elise
no.
juan
It depends on how someone sees anxiety.
Elise
depression &substance use
Shawnasie
it has a co acerance in both up to 60%
Shawnasie
Diagnosed anxiety along with depression are apart of post traumatic stress disorder previously known as shell shock... now "shock" often comes on instantly, hence the name. A natural reaction to a specific chemical imbalance, Like when people are extremely happy, sad or sometimes even angry they cry
Luci
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