SLC S23 Week4 || Quadrilaterals
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| Assalamualaikum |
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Hello steemians!
It's me @fazal-qadir from Pakistan
I hope you guys will be safe and sound. Another week with challenging contest. I will try my best to accurately answer of each section! With diagram, explanation and with diagrams.
Thanks to Sir @sergeyk for bringing another challenging task this week. I am hoping I will do better this time. .
Let's start from here.
Quadrilaterals and Their Properties.
Quadrilateral:
A polygon which have four sides are called quadrilateral.
Types of Quadrilaterals:
Two major types of quadrilateral:
a). Parallelogram
b). Trapezoid
The following three are sub types of parallelogram
- Rectangle.
- Rhombus.
- Square.
Build a parallelogram, demonstrate its elements and properties.
Parallelogram
Parallelogram have four sides all are parallel to each other.
Properties:
1). Opposite sides are parallel
2). Opposite sides are equal in length.
3). Opposite angles are equal .
4). Both diagonal bisect each other.
5). Any two consecutive angles are supplementary ( 180 °).
- Opposite sides are parallel.
Diagram part:
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Explanation:
As you can see from the figure above the alternate angles of Side AB and side CD is <CDA is = 28 ° also <BAD is = 28°. Both angles are equal whicb means that when two sides alternate angles are equal than the side are parallel to each other.
So side AB is parallel to CD, also AC side is parallel to BD vice versa.
- Opposite sides are equal in length.
Diagram part:
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Explanation:
As you can see from the figure, the side AB and the side CD which is parallel to each other. Length of both side is = 5 cm . The sides AC and BD is = 3 cm.
Hence it's prove that parallelogram opposite sides are equal in length.
- Opposite angles are equal .
Diagram part:
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Explanation:
As you can see from the above figure, the opposite angles of this figure are equal to each other . Angle C is equal to angle B. When. We change the position of one vertex the both angles chances simultaneously. Also the angle A is Equal to angle D. Same rule will apply here. When we move the angle A the value will change on both vertices.
In this figure value of angles C and Angle B is equal to =121.4° while angles on A and D are also equal which is equal to 58.6 °
4.Both diagonal bisect each other.
Diagram part:
Explanation:
As you can see from the diagram. Both diagonal have bisect each other. The value of length AE is equal to ED. Same as, the value of CE is equal to EB. Hence it's proved that both the diagonals of parallelogram bisect each other.
5.Any two consecutive angles are supplementary ( 180 °)
Diagram part:
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Explanation:
As we look at the figure above. When we add the angle A and angle B which are consecutive angles . After adding the result comes 180° . It's shows that when two consecutive angles added it become supplementary angle.
Caluculation:
63.4+116.6= 180°
| GIF |
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| Combination of all properties |
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Build a trapezoid, demonstrate its elements and properties.
Trapezoid:
" A trapezoid is a quadrilateral, which has only two sides are parallel to each other. "
Trapezoid types and properties
It has three main types.
- Arbitrary trapezoid also called general trapezoid.
- Right trapezoid ( one angle is 90 between one parallel and non parallel side)
- Isosceles trapezoid (non parallel sides are equal ).
Arbitrary trapezoid.
Properties:
- only two sides are parallel to each other.
- Parallel sides are called base
- non parallel sides are called legs.
- diagonals are not perpendicular
- all angles are changed non of them are equal to 90°
Diagram
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Explanation
As we can see from the above diagram. AB and CD sides are parallel to each other these sides are called base of trapezoid. While Side AC and BD sides are legs of trapezoid and they are non parallel sides.
All the non parallel sides(legs) are not equal to each other.
| GIF |
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| YouTube link |
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Right trapezoid
Properties:
- Only two sides are parallel
- parallel sides are called base
- non parallel sides are called legs
- non parallel sides are not equal
- it has only one pair of right angled(90°) b/w parallel and non parallel sides.
Diagram
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Explanation
As we can see from the diagram. Only Two sides like AB is parallel to CD side The length of both non parallel sides are not equal. Only one pair from non parallel side and parallel sides makes one angle equal to 90.
| GIF |
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| YouTube Link |
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https://youtube.com/shorts/PaepgtnyS8M?si=tR1XgfcLzBY6FYU7
Isosceles trapezoid.
Properties:
- Only two sides are parallel that sides are called base
- two sides are non parallel that sides are called legs.
- length of both non parallel sides are equal.
- Both Diagonals are equal in length
Diagram
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Explanation:
As we can see from the diagram two sides AB is parallel to DE. The non parallel sides AD and BE is equal in length. The angles formed b/w parallel and non parallel sides are equal.
| GIF |
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| YouTube |
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Build a rhombus, demonstrate its elements and properties.
Rhombus:
In rhombus all sides are equal , opposite sides are parallel
Properties:
- All sides are equal in length
- opposite side are parallel
- two consecutive angles are supplementary
- diagonal bisect each other
- diagonals are perpendicular
- either diagonal bisect the opposite angles
Diagram:
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Explanation:
As you can see from the above diagram, all four sides are equal in length. If we measure the connective angles it becomes supplementary (180°). Diagonals bisect each other as you can see both values are same. Diagonals also bisect the opposite angles .
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Build a rectangle, demonstrate its elements and properties.
Rectangle:
Rectangle is a parallelogram, in which all the internal angles are equal to 90° , opposite sides are equal in length.
Properties.
- opposite side of a rectangle are Equal
- all four sides are parallel
- opposite angles of rectangle are equal
- consecutive angles are equal to 180° ( supplementary)
- diagonal of rectangle bisect each other
- diagonal of rectangle are equal in length.
Diagram:
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Explanation:
As we can see from the diagram, opposite side of rectangle are equal. All the internal angles are equal to 90°. The two consecutive angles are equal to 180° . The length of both bisector are equal.
The opposite angles of rectangle are also equal.
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Build a square, demonstrate its elements and properties.
Square:
Square is a parallelogram, whose all sides are equal in length. All the internal angles are equal to 90° .
Properties:
- all sides are equal in length.
- all internal angles are equal to 90°
- sum of all internal angles is equal to 360°.
- Diagonal bisect each other.
- Diagnol are perpendicular
Diagram:
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Explanation:
As we can see from the diagram, All sides are equal in length. All the internal angles are Equal to 90° . If we add all the angles it will be equal to 360°.
Both diagonal bisect each other at point F. Both diagonals are perpendicular to each other.
| GIF |
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| YouTube link |
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https://youtube.com/shorts/qt4j7TVUTx8?si=X6TfjQjDzxMeAjV4
I want to invite my friends in this competition.
@muhammad-ahmad
@iqlimaa
And
@dequeen
Best regards
@fazal-qadir
