+561 An isosceles trapezoid has side lengths 13,4,13 and 14. What is the perimeter of its Varignon parallelogram?
+118687 An isosceles trapezoid has side lengths 13,4,13 and 14. What is the perimeter of its Varignon parallelogram?
I have decided to practice my descriptive skills.
It is important that you develope your comprehension skill in geometry descripions. SO draw what I am describing and see if you can make sense of it. If you cannot then ask and I will present some diagrams. BUT if you try hard enough you probably will not need a diagram.
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Draw the isosceles trapezoid so that the longest side is on the bottom of the pic
You will see that the diagonals of the varigon parallelogram cross at right angles. So it is not just a parallelogram it is also a rhombus. You only need to find one side because they are all the same.
If you cut your trapezium into three it is made up of a central rectangle that is height by 4 units
and 2 congruent right angled triangles that are have a hypotenuse of 13 and one other side 5.
Using pythagoras's theorum it is easy to determine that the height is 12. This is the length of one of the diagonals.
Now consider the one of the congruent triangles.
Half the base is included in the other diagonal and the other half of it is not.
The base is 5. so 2.5 is inincluded in the other diagonal. But there are two right triangles so 2.5*2=5 units from the bas are NOT in the other diagonal.
So the diagonal is 14-5=9 units
So the two diagonals of the varignon rhomus are 9 and 12
The half diagonals are 4.5 and 6 units.
Using pythagoras again the legtn of the side of the rhombus will be 7.5 inits
So the perimeter will be 4*7.5 = 30units
+118687 An isosceles trapezoid has side lengths 13,4,13 and 14. What is the perimeter of its Varignon parallelogram?
I have decided to practice my descriptive skills.
It is important that you develope your comprehension skill in geometry descripions. SO draw what I am describing and see if you can make sense of it. If you cannot then ask and I will present some diagrams. BUT if you try hard enough you probably will not need a diagram.
-----------
Draw the isosceles trapezoid so that the longest side is on the bottom of the pic
You will see that the diagonals of the varigon parallelogram cross at right angles. So it is not just a parallelogram it is also a rhombus. You only need to find one side because they are all the same.
If you cut your trapezium into three it is made up of a central rectangle that is height by 4 units
and 2 congruent right angled triangles that are have a hypotenuse of 13 and one other side 5.
Using pythagoras's theorum it is easy to determine that the height is 12. This is the length of one of the diagonals.
Now consider the one of the congruent triangles.
Half the base is included in the other diagonal and the other half of it is not.
The base is 5. so 2.5 is inincluded in the other diagonal. But there are two right triangles so 2.5*2=5 units from the bas are NOT in the other diagonal.
So the diagonal is 14-5=9 units
So the two diagonals of the varignon rhomus are 9 and 12
The half diagonals are 4.5 and 6 units.
Using pythagoras again the legtn of the side of the rhombus will be 7.5 inits
So the perimeter will be 4*7.5 = 30units
+118687 Do I need to?
I was practicing my skill at description. I think I did alright :)
Actually Chris, try following my instructions with a pen and paper.
If you really find it confusing then I will do a pic but honestly, if you think about what I have written I think (hope) that it is fairly easy to follow.
Please give it a go and let me know ://
OH!
I did have to look up what a Varignon parallelogram was.
Here is what I found :)
"
Varignon Parallelogram
Midpoints of successive sides of a quadrilateral form a parallelogram. To see this, observe that the lines in question are parallel to the diagonals of the quadrilateral. They are therefore pairwise equal and parallel. This is known as the Varignon parallelogram. "
