SLC S23 Week4 || Quadrilaterals
Assalamualaikum my fellows I hope you will be fine by the grace of Allah. Today I am going to participate in the steemit learning challenge season 23 week 4 by @sergeyk under the umbrella of steemit team. It is about Quadrilaterals. Let us start exploring this week's teaching course.
Geogebra Build a parallelogram, demonstrate its elements and properties.
To build the parallelogram I took 3 points A, B, and C. I used segment to connect point A to point B and point B to C. I drew a parallel line to BC using the parallel line tool. Then I drew a parallel line to AB. I found the point of intersection D of these two parallel lines. I hide parallel lines and connected the points to get the parallelogram.
Elements and Properties
The opposite sides are equal in length. I measured the distance of all the sides and it is sure that opposite sides of the parallelogram are equal in length.
The opposite angles of the parallelogram are also equal. The angles A and C are equal and similarly the angles B and D are equal. Sum of all the 4 angles is equal to 360.
The diagonals of the parallelogram bisect each other. The length measurements hows they bisect each other and their point of intersection is the midpoint. The diagonal AC has length of 6.2 and the bisection shows the half has length 3.1. The diagonal BD has 9.7 and DE and BE has half length of BD.
The area of the parallelogram is given by this formula: Area = base x height.
Build a trapezoid, demonstrate its elements and properties.
To build trapezoid I took 3 points by following the teacher. I used the segment tool to connect the point A to D and A to B. I took a parallel line to AD passing through the point B. On this parallel line I took a point C. I hide the parallel line and connected the point B to C with segment and then C to D with a segment.
Elements and Properties
- The parallel sides of the trapezoid are called the bases.
- Non parallel sides are called legs.
- The smallest distance between the two bases is called the height.
- In this shape of trapezoid the height is AB.
The line which joins the mid point of the both the legs is called the midsegment of the trapezoid. The midsegment of trapezoid is given by: Midesegment Length = ( Base1 + Base2 )/2.
The interior sum of all the angles of the trapezoid is always 360. Here the sum of the of 95 + 52 + 128 + 85 = 360.
Consecutive angles formed by the bases and the legs are supplementary means their sum is 180. In the trapezoid shape it can be seen that the sum of 52 + 128 = 180 and similarly the sum of 95 + 85 = 180.
In the isosceles trapezoid the length of the non parallel sides is equal and the base angles are also equal. Whenever the non-parallel sides length is equal then the base angles are equal. The AB and CD length is equal and similarly the values of the angles.
In the isosceles trapezoid the length of the diagonals is equal to each other. The length of AC is equal to length of BD. But in a general triangle the length of the diagonals is not equal.
The area of the trapezoid is given by this formula: A = 1/2 (Base1 + Base2) x Height.
If we rearrange the legs parallel to each other we can form a parallelogram from this trapezoid. The sum of the internal angles is always 360.
Build a rhombus, demonstrate its elements and properties.
I took a line segment AB. I used circle with center and radius tool to build a circle with center A and radius AB and similarly I build another circle with center B and radius AB. I found the point of intersections of both the cirlce. Then I used polygon tool to connect the points and a rhombus formed. I measured the angle of the rhombus and it is 90. It always remains same whether the size of the rhombus increases or decreases.
Elements and Properties
- All the sides of the rhombus are equal in length.
- All the opposite angles are equal.
- The diagonals bisect each other at the right angle.
- Diagonals bisect the angles into two equal parts.
- The sum of the internal angles is 360. Sum of the angles half of the rhombus is always 180.
- The area of the rhombus is given by this formula: Area = 1/2 x d1 x d2. In this formula d1 and d2 are the lengths of the diagonals.
- The diagonals of the rhombus are usually not always equal in length.
Build a rectangle, demonstrate its elements and properties.
I took two points and connected them with segment. I got one side of the rectangle AB. I drew perpendicular line to AB from point A and point B. I took a point on the perpendicular line. I constructed a parallel line to AB passing through the point C. I found the point of intersection D of the other perpendicular line ad parallel line. Rectangle has formed now. I removed the helping lines and used segments.
Elements and Properties
- The opposite sides of rectangle are equal in length.
- All the angles of the rectangle are of 90 degree.
- The length of the diagonals are equal.
- Midpoints of the diagonals are at the same point. At this point they intersect each other.
- The diagonals bisect each other.
- Area of rectangle = length x width
- Perimeter of rectangle = 2 ( length + width )
- The line parallel to the widths passing through the mid points converts the rectangle into two equal parts and each part is a new rectangle.
- Sum of the interior angles is 360 degree.
Build a square, demonstrate its elements and properties.
I took a line segment AB. I constructed two perpendicular lines on both the points A and B. I used circle with center and radius tool to build a circle on A with radius AB and on point B with same radius. I found the point of intersections. I used polygon tool to combine the points to build the square.
I constructed the same square in just two steps by using regular polygon tool. I took two points and in the popup I gave 4 vertices and square is ready.
Elements and Properties
- The distance of all the sides of the square is equal in length.
- All the angles of the square are of 90 degree.
- The length of the diagonals is equal.
- They intersect at each other at their midpoints.
- Diagonals bisect each other at right angle.
- The line parallel to the sides passing through the mid points converts the square into two equal parts and each part is a rectangle. If we pass two lines from the midpoints of the other side then the complete square will be divided into 4 equal squares.
- Area of square = side x side
- Perimeter = 4 x sides
- The sum of all the angles is 360 degree.
This is all about the quadrilaterals with their different elements and properties. I invite @wuddi @chant and @suboohi to join this learning about the quadrilaterals with geogebra.
Upvoted! Thank you for supporting witness @jswit.