# 4.2 Understanding quadrilaterals and their properties in problems

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## Understanding quadrilaterals and their properties in problems

ACTIVITY 1

To apply understanding of quadrilaterals and their properties in problems

[LO 3.7, 4.4]

• All the figures for this section are on a separate problem sheet. Use it together with the questions that follow here.
• Work in pairs as follows: first study each problem independently until you have solved it or gone as far as you can. Then explain your solution carefully, and step by step, to your partner, until he understands it well enough to write it down. In the following problem it will be your partner’s turn to explain his solution to you for writing down. You should remember to give a reason or explanation for everything you do.

1. Calculate the values of a, b, c , etc. from the information given here and in the sketch, and answer the question.

1.1 The diagram shows a square with one side 3 cm. a = an adjacent side.

b = the diagonal. c = the area of the square.

Why does the diagonal make a 45 ° angle with the side?

1.2 A rhombus is given, with long diagonal = 8 cm and short diagonal = 6 cm. a = side length.

b = area of rhombus..

Why are you allowed to use the Theorem of Pythagoras here?

1.3 The diagram shows a rectangle with a short side = 5 cm and a diagonal = 13cm.

a = the long side. b = area of rectangle.

Why is the other diagonal also 13 cm?

1.4 The figure is a parallelogram with one internal angle = 65°, height = 3 cm and long side = 9 cm.

a = smaller of internal angles. b = larger of internal angles. c = area of parallelogram

Explain why this parallelogram has the same area as a 3 cm by 9 cm rectangle.

2. Calculate the value of x from the information in the sketches.

2.1 An equilateral triangle is given, with side 15 cm and area = 45 cm 2 . x = height of triangle.

Why does this triangle have a 60 ° internal angle?

2.2 The diagram shows a trapezium with longest side 23 cm and the side parallel to

it 15 cm and height = 8 cm.

x = area of trapezium.

Why are the two marked internal angles supplementary?

2.3 The figure is a kite with area 162 cm 2 and a short diagonal of 12 cm. x = long diagonal.

Why do the internal angles of the kite add up to 360 ° ?

2.4 The sketch shows the kite from question 2.3 divided into 3 triangles with equal areas (ignore the dotted line). x = top part of long diagonal.

3. These problems require you to make equations from the information in the sketch, using your knowledge of the characteristics of the figure. Solving the equations gives you the value of x .

3.1 The figure is a rhombus with two angles marked 3 x and x respectively.

Why can’t we call this figure a square?

3.2 In the parallelogram, two opposite angles are marked x + 30° and 2 x – 10° respectively.

Explain why the marked angle is 110 ° .

3.3 The trapezium shows the two marked angles with sizes x – 20° and x + 40° respectively.

Why is this not a parallelogram?

3.4 Given is a rhombus with the short diagonal drawn; one angle made by the diagonal is 50° and one internal angle of the rhombus is marked x .

Shape sheet

Problem sheet

## 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: 3.2 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: 3.2.2 transformations. 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; 3.6 recognises and describes geometric solids in terms of perspective, including simple perspective drawing; 3.7 uses various representational systems to describe position and movement between positions, including:ordered grids LO 4 MeasurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. We know this when the learner: 4.4 uses the theorem of Pythagoras to solve problems involving missing lengths in known geometric figures and solids.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
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?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
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Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
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anybody can imagine what will be happen after 100 years from now in nano tech world
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silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
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