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Mathematics

Grade 9

Algebra and geometry

Module 8

Geometry of lines and triangles

Activity 1

To learn conventions of naming sides and angles in triangles

  • Refer to the triangle alongside to understand the terms.
  • The three sides of the triangle are called AB, AD and BD.
  • We often name a side in a triangle by using the small letter of the name of the opposite corner. The corners (vertices) of the triangle are named by using capital letters.
  • When A or A ˆ size 12{ { hat {A}}} {} is used, it refers to the a ngle made by side BA and side AD.
  • For the angle one can also say BAD or B A ˆ D size 12{B { hat {A}}D} {} .
  • But if I say A=38°, it is clear what I mean.
  • We refer to triangle ABD or ΔABD, writing the letters in alphabetical order.

Exercise:

To show that you understand the naming

conventions, draw the following triangle in the space

to the right:

Draw ΔQRT with q=4cm, T=65° and QT=5,5cm.

You should notice that you don’t need to be told

the length of t, nor the sizes of Q ˆ size 12{ { hat {Q}}} {} or R ˆ size 12{ { hat {R}}} {} . First

draw a rough sketch and fill the details in on that

sketch to help you plan your drawing.

Assignment:

You should already know that triangles are classified according to their shape. Make an A4–sized poster for your own use, clearly showing the characteristics of the following types of triangle: equilateral, right–angled, isosceles and scalene. Name the vertices and sides according to the conventions above. You must work as accurately and neatly as you can.

Measure the sides and the angles of your triangles and fill these measurements in on your poster.

Activity 2

To develop the principle of congruence in triangles

[LO 4.4, 3.3, 3.5]

  • In the previous exercise you drew ΔQTR from specifications given to you. Ask the other learners who did this exercise to show you their drawings, and check whether their triangles agree perfectly with the sizes given in the question. Measure the side and the two angles not specified, to see whether they also agree with yours.
  • You should find that all triangles drawn by anybody according to the instructions, are always identical. In fact, it is impossible to draw that triangle so that it is different! Write down, with a partner, why you think this is the case.
  • Here are more descriptions of triangles. See whether the same happens with them – in other words, that it is impossible to draw different triangles that fit the same description. Again, write down your view of each situation. The last one is quite difficult to draw – try it!
  • Draw ΔAGE with a=4cm, E=90° and AG=5cm.
  • Draw ΔNOH with HN=4cm, H=56° and O=72°.
  • Draw ΔBAT with B=48°, T=65° and A=67°.
  • Draw ΔMOD with m=5,5cm, O=65° and DM=4cm.
  • Draw ΔAMP with a=4,2cm, m=5cm and p=5,6cm.
    • In each of the above triangles, only three of the six sizes (three sides and three angles) were specified in the question. And sometimes that was enough to ensure that everyone drew identical triangles. But in ΔBAT and ΔMOD the three items were not enough to ensure identical triangles from everyone.
    • So, when is it enough? Maybe you have already discovered the secrets:

ΔQRT: Two sides and the angle between them were specified.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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