Quadrilaterals

[Njabs]

I am a College student, we are studying Euclidean geometry. Currently we are busy with constructions, our lecturer argued that we can change one quadrilateral into another by changing some properties and keeping other properties unchanged. Four questions came up:

1. Explain how you must change diagonals the of a kite so that the kite becomes a rhombus.
2. Explain how you must change the diagonals the diagonals of a rhombus so that the rhombus becomes a square
3. Explain how you must change the diagonals of a square so that the square becomes a rectangle
4. Explain how you must change the diagonals of a rectangle so that the rectangle becomes a parallelogram
5. Explain how you must change the diagonals of a parallelogram so that the parallelogram becomes an isosceles trapezium

I find these questions vague, unfortunately our lecturer is a difficult man. According to my understanding, for example, in both the kite and the rhombus, diagonals intersect at 90 degrees, so what difference will it make. May be the problem is with me. I do not understand how to answer these questions. Somebody help please, how do I answer these questions. Thank you for your time!

 

[Deleted member 4993]

I am a College student, we are studying Euclidean geometry. Currently we are busy with constructions, our lecturer argued that we can change one quadrilateral into another by changing some properties and keeping other properties unchanged. Four questions came up:

1. Explain how you must change diagonals the of a kite so that the kite becomes a rhombus.
2. Explain how you must change the diagonals the diagonals of a rhombus so that the rhombus becomes a square
3. Explain how you must change the diagonals of a square so that the square becomes a rectangle
4. Explain how you must change the diagonals of a rectangle so that the rectangle becomes a parallelogram
5. Explain how you must change the diagonals of a parallelogram so that the parallelogram becomes an isosceles trapezium

I find these questions vague, unfortunately our lecturer is a difficult man. According to my understanding, for example, in both the kite and the rhombus, diagonals intersect at 90 degrees, so what difference will it make. May be the problem is with me. I do not understand how to answer these questions. Somebody help please, how do I answer these questions. Thank you for your time!

1. In a rhombus, the diagonals bisect each other at 90°

2. In a square, the diagonals are congruent.

and so on....

 

[wjm11]

I am a College student, we are studying Euclidean geometry. Currently we are busy with constructions, our lecturer argued that we can change one quadrilateral into another by changing some properties and keeping other properties unchanged. Four questions came up:

1. Explain how you must change diagonals the of a kite so that the kite becomes a rhombus.
2. Explain how you must change the diagonals the diagonals of a rhombus so that the rhombus becomes a square
3. Explain how you must change the diagonals of a square so that the square becomes a rectangle
4. Explain how you must change the diagonals of a rectangle so that the rectangle becomes a parallelogram
5. Explain how you must change the diagonals of a parallelogram so that the parallelogram becomes an isosceles trapezium

I find these questions vague, unfortunately our lecturer is a difficult man. According to my understanding, for example, in both the kite and the rhombus, diagonals intersect at 90 degrees, so what difference will it make. May be the problem is with me. I do not understand how to answer these questions. Somebody help please, how do I answer these questions. Thank you for your time!

Think about the relative lengths of the various diagonals in question. Are they the same or different?
Next, think about how they intersect each other. Does one bisect the other? Are both diagonals bisected? Are neither bisected?
And if neither are bisected, is there still something you can state about how they intersect each other? Are they congruent? Are the intersected components congruent?

 

[Njabs]

Thanks

Thank you guys for your input, I really appreciate that. I was not sure whether the question has to do with midpoints of the different geometric figures.

 

[Bob Brown MSEE]

Your teacher believes that this exercise is clear, because when he was a boy he made kites from scratch.

To make a kite
https://www.youtube.com/watch?v=Z2QLdTiOU3c

The two sticks are the diagonals to which your teacher is referring.
The string rapped all the way around the kite, starting at the bottom and ending at the bottom is the quadrilateral to which your teacher is referring.

 

[Njabs]

Thanks

Your teacher believes that this exercise is clear, because when he was a boy he made kites from scratch.

To make a kite
https://www.youtube.com/watch?v=Z2QLdTiOU3c

The two sticks are the diagonals to which your teacher is referring.
The string rapped all the way around the kite, starting at the bottom and ending at the bottom is the quadrilateral to which your teacher is referring.

Thanx Bob I doubt though he had that on his mind when he asked the question!