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Which of the following statements are true?

(A) If a kite is also a parallelogram, then it must be a rhombus.
(B) If a trapezoid is also a parallelogram, then it must be a rhombus.
(C) If a trapezoid is also a kite, then it must be a parallelogram.
(D) If a rhombus is also a trapezoid, then it must be a kite.

 Jan 3, 2017

Best Answer 

 #2
avatar+561 
+11

A is incorrect

You can choose more than 1 option

 Jan 3, 2017
 #1
avatar+23 
-1

A :p

 Jan 3, 2017
 #2
avatar+561 
+11
Best Answer

A is incorrect

You can choose more than 1 option

arnolde1234  Jan 3, 2017
 #3
avatar+23 
-1

ummmmm.... C and D. idk ._.

 Jan 3, 2017
 #4
avatar+561 
+6

Incorrect

arnolde1234  Jan 3, 2017
 #5
avatar+118673 
+1

A and C are both true   

(I haven't formally proved it which I should do  for absolute certainty)

 

I think for C it has to be a rhombus as well.

I think what you call a trapezoid, I would call a trapezium and all rhombuses are trapeziums.

Just as all rhombuses are paralellograms.

 Jan 4, 2017
 #6
avatar+561 
+6

Apperently, A and C are wrong.

 

C alone is wrong too.

arnolde1234  Jan 4, 2017
 #7
avatar+118673 
+1

Here is one problem with this question.

 

According to several sources on the net a trapexium is the same thing as a trapezoid BUT

according to Wolfram|Alpha, and I quote

"There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British (AND AUSTRALIAN)  definition is a quadrilateral with two sides parallel (e.g., Bronshtein and Semendyayev 1977, p. 174)--which Americans call a trapezoid."

 

So before all these answers can be accepted or rejected we may have to agree upon a defintion of a trapezium or trapezoid!

 

However, A is still definitely correct  :)

Melody  Jan 4, 2017
 #8
avatar+118673 
+1

I suppose I should at least give reasons

 

(A) If a kite is also a parallelogram, then it must be a rhombus.

With Kites and rhombuses the diagonals MUST intersect at right angles.

Parallelograms have opposite sides parallel.

A parallelogram where the diagonals interect at right angles is a rhombus

So A is DEFINITELY correct


(B) If a trapezoid is also a parallelogram, then it must be a rhombus.

All parallelograms are trapeziums (they have at least one pair of parallel sides)

so If a trapezoid is also a parallelogram it can be ANY parallelogram

so B is false

 



(C) If a trapezoid is also a kite, then it must be a parallelogram.

This one depends on the definition of a trapezoid.  Using the American definition it is definitely false.

Using the English (and Australia) definition it is true but it is harder to prove.

 


(D) If a rhombus is also a trapezoid, then it must be a kite.

All rhombuses are trapeziums. end of story. false

Melody  Jan 4, 2017
 #9
avatar+561 
+8

The correct answer to the questiond is:

 

A, C, D

 Jan 5, 2017

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