SLC S23 Week4 || Quadrilaterals

_{Image taken from Pixabay}

Another week, another challenge from @sergeyk, this time we have Quadrilaterals, if you want to join it's not too late, you can check the full post and how to participate in the following post SLC S23 Week4 || Quadrilaterals

Let's get started!

• Build a parallelogram, demonstrate its elements and properties.

To create a parallelogram I used the guide @sergeyk presented in the course, started with 3 points, placed a parallel line through point A to BC and then another parallel through point C to AB.

I added some stylization and pointed out the elements and properties, here is a live GIF example:

Properties & Elements

• Four vertices (A, B, C, D)
• Four sides: Opposite sides are equal and parallel (AB = CD, AD = BC)
• Two pairs of opposite angles (∠BAC = ∠BCD, ∠ABC = ∠ADC)
• Two diagonals (AC, BD)
• Opposite angles are equal.
• Consecutive/Adjacent angles are supplementary (sum to 180°).
• Diagonals bisect each other (AF = FC, BF = FD).
• The sum of all interior angles is 360°.
• Each diagonal divides the parallelogram into two congruent triangles

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• Build a trapezoid, demonstrate its elements and properties.

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Let's split the trapezoid in the 3 cases, we have:

Arbitrary Trapezoid

Again I used the @sergeyk's tutorial from the class to create the arbitrary trapezoid and marked it accordingly, let's see the elements and properties.

Elements & Properties:

• Four vertices (A, B, C, D)
• Four sides: Two sides are parallel (AD,BC) two are non-parallel (AB,CD)
• Two legs (BA, CD)
• Two bases (BC, AD)
• Two diagonals (AC, BD)
• Height (BE)
• Only one pair of sides are parallel
• Sum of interior angles is 360 degrees
• The mid segment, the line that connects the mid of trapezoid's legs is parallel to the bases and equals the average lengths of bases

Right Trapezoid

In this case I started with a segment to which I drew a parallel line. Now these two being parallel I drew another line from one point perpendicular to the opposite side making sure I create the two 90 degree angles, now this was almost done, connected the last two points to create the trapezoid. Now all that was left was to stylize it and point it's properties and elements, here's a small GIF with me building it:

And also here is a GIF from Geogebra moving the trapezoid's shape:

Elements & Properties

• Four vertices (A, B, C, D)
• Four sides: Two sides are parallel (AB,CD) two are non-parallel (AC,BD)
• Two legs (AC, DB)
• One of the legs is perpendicular to the base (DB)
• Two bases (CD, AB)
• Two diagonals (AD, BC)
• Height (CG) & (DB could also be considered)
• Two Angles at 90 degrees (<ABD) and (<CDA)
• Only one pair of sides are parallel
• Sum of interior angles is 360 degrees with two being 90 degrees
• The mid segment, the line that connects the mid of trapezoid's legs is parallel to the bases and equals the average lengths of bases
• The height's length is the same as the perpendicular leg

Isosceles Trapezoid

This is where the fun begins, I will start by showing you a GIF on how I achieved my Isosceles Trapezoid and then explain it in a few sentences below, the GIF is 1 Minute Long!.

Had to upload it via Giphy as it was too big to upload directly here!

I started with a segment to which I drew a perpendicular line to each point to help me create the top base. I added a point to the first perpendicular line and from this point I created a parallel line to the base. Now all I had to do was create the intersection of the last perpendicular with the top base.

With the two bases ready I took a random point on the top one and drew a segment to the point on the base, the left leg to be more precise, and we are going to use it's length to create a circle from the other point of the bottom base with the radius equal to the length of the left leg. The intersection of the circle with the top base will be the last point we need to create an isosceles trapezoid. The GIF describes it better than words.

Here's another representation with it's elements and properties:

Elements & Properties

• Four vertices (A, B, C, D)
• Four sides: Two sides are parallel (AB,CD) two are non-parallel but equal (AC,BD)
• Two legs which are equal (AC, DB)
• Two bases (CD, AB)
• Base angels are equal (<A = <B) & (<C = <D)
• Two diagonals that are equal (AD, BC)
• Height is perpendicular to the base (CG)
• Only one pair of sides are parallel
• Legs are equal
• Sum of interior angles is 360 degrees
• The mid segment, the line that connects the mid of trapezoid's legs is parallel to the bases and equals the average lengths of bases

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• Build a rhombus, demonstrate its elements and properties.

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Let's start again with the GIF again:

This was far easier to create then the previous task, here I started with a segment on which I created a circle with the radius equal to thesegment, drew a second radius, at this point I had half a rhombus.

Next I created a circle from both edges of each segment with radius length reaching the first circle's center, and the intersection of these two new circles will be the last point of our rhombus. From this point I completed the shape and stylize it, here is a final result.

Also a close up picture so you can also see the bisectors better:

Elements & Properties

• Four vertices (A, B, C, D)
• Four equal sides (AB, AC, BD, CD)
• Two diagonals that bisect each one perpendicularly (AD, BC)
• Opposite angles are equal (<A = <D) & (<B = <C)
• All four sides are equal
• Diagonals bisect each other creating 90 degree angles
• Diagonals also bisect the angles of the rhombus
• Sum of interior angles is 360 degrees

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• Build a rectangle, demonstrate its elements and properties.

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After the previous creation rectangle feels so much easier, here is a quick draw of it in a GIF:

Started with a bottom segment, on each point I added a perpendicular line, on the first perpendicular I added a point through which I created a parallel line to the first segment.

Now the intersection of the second perpendicular line with the top parallel is the last point of our rectangle.

With some stylization the final result looks like this:

Elements & Properties

• Four vertices (A, B, C, D)
• Four sides: opposite ones are parallel and equal
• Four right angles (<A, <B, <C, D)
• Two equal diagonals that bisect each other (not in a 90 degree angle)
• Opposite sides are equal and parallel
• 90 degree interior angles
• Sum of interior angles is 360 degrees

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• Build a square, demonstrate its elements and properties.

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For the last task I created the Square using a segment two perpendicular lines and a circle, the circle created from point A with the radius equal to AB helps us create the even sides and paired with the perpendicular and parallel tools we get the 90 degrees, exactly what we need for a square, here is a short GIF that shows how I made it:

And a stylized representation:

A quadrilateral is a Square if it has the opposite sides parallel, the sides equal and all angles measure 90 degrees.

Elements & Properties:

• it has 4 sides
• it has 4 vertices
• all four sides are equal to each other
• interior angles measure 90 degrees each
• length of diagonals is equal, they also bisect each other
• the diagonals cut the square in two congruent triangles

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I tried to make the explanations as understandable as I could, that's why I also added the creation process in some cases, these will surely help along the text.

That's all for this challenge, in the end I'd like to invite @mojocioio, @r0ssi and @titans, mojo will surely enjoy this new challenge.

Thank you and I am wishing you good luck if you want to participate. Have a great day!