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October 23rd, 2019, 07:44 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 675 Thanks: 88  Does A Quadrilateral With Three Congruent Sides Have To Be A Trapezoid?
A quadrilateral with three congruent sides can be a trapezoid with one horizontal side and both diagonals congruent where there would be a vertical line of symmetry. Does a quadrilateral with three congruent sides have to be a trapezoid?

October 23rd, 2019, 08:08 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 
A trapezoid is formed if the two angles between each pair of adjacent congruent sides are congruent. What if those same two angles are not congruent? 
October 24th, 2019, 05:49 AM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 675 Thanks: 88 
I guess it doesn't have been a trapezoid. I attached a quadrilateral I drew attempting to make the three sides other than the bottom be congruent.

October 24th, 2019, 08:05 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677  

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congruent, quadrilateral, sides, trapezoid 
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