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Hey! I have a question for this problem:

 

In quadrilateral PQRS, sides PS and QR have equal length and sides PQ and RS are parallel to each other. Point X is the intersection of the diagonals PR and QS. Which of the following conclusions must be true?

A) triangle PXQ is congruent to triangle RXS
B) triangle SPR is congruent to triangle RQS
C) triangle SPQ is congruent to triangle QRS

 

I believe it's A and C, but I'm not sure. can someone confirm?

 Sep 16, 2021
 #1
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That's right, it's (A) and (C)!

 Sep 16, 2021
 #2
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It's not A and C...

Guest Sep 16, 2021
 #3
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Draw a pic. of a random quadrilateral.   One that does not look very special

Call it PQRS

Mark on it the things that are told to you.

Redraw it so that it looks more like it is supposed to.  But do not give it extra special features that are no specified (unless it is unavoidable)

What shape is it?

 

Now test all those possibilities and you will see that only one seems right.

 Sep 17, 2021
 #6
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All of them?

Guestatbest  Sep 18, 2021
 #8
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No not all.

Melody  Sep 18, 2021
 #9
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hmm, then only A and B

Guestatbest  Sep 18, 2021
 #4
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It's only C !!!

Square         ✓

Rectangle     ✓

Trapezoid      ✓

Rhombus       ✓

Parallelogram     ✓

 Sep 17, 2021
 #5
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Your shapes are right.

The most general one is the Trapezoid  (In Australia we would call it a trapezium)

 

But unfortunately, your conclusion is not correct.   (unless I have made some really stupid error)

 

Draw your trapezoid and re-check your result     laugh

Melody  Sep 17, 2021
 #7
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Sorry.   I answered this yesterday but it had been autoblocked and  I did not realize.

Melody  Sep 18, 2021

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