Consider regular pentagon ABCDE . If diagonal is drawn, then a quadrilateral ACDE is formed. Being as specific as possible, what type of quadrilateral is ACDE ?
A)parallelogram
B)kite
C)trapezoid
D)isosceles trapezoid

Question

Consider regular pentagon ABCDE . If diagonal  is drawn, then a quadrilateral ACDE is formed. Being as specific as possible, what type of quadrilateral is ACDE ?
A)parallelogram 
B)kite 
C)trapezoid 
D)isosceles trapezoid

Quizplus · Accepted Answer

A diagonal of a pentagon creates two separate triangles and a quadrilateral. Since pentagons are not parallelograms or kites, the only possible quadrilaterals that could be formed are trapezoids or isosceles trapezoids. However, since diagonal 11ebfb55_24a8_3ff5_9d86_510748a95e4c_TBX8811_11 splits diagonal CE evenly and diagonal AC and diagonal DE are congruent, we know that ACDE must be an isosceles trapezoid.

Consider Regular Pentagon ABCDE