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Choose the item whose diagonals need not be congruent (A) Rectangle      (B)...

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novjb | Salutatorian

Posted September 4, 2013 at 11:45 PM via web

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Choose the item whose diagonals need not be congruent

(A) Rectangle      (B) isosceles trapezoid   (C) square     (D) rhombus

Choose the item whose diagonals bisect each other.

(A) rhombus       (B) trapezoid   (C) kite    (D) isosceles trapezoid 

Thank you for your help.

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted September 4, 2013 at 11:57 PM (Answer #1)

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Diagonals must not be congruent?

Since rectangle has 2 pairs of equal opposite sides and perpendicular sides, the diagonals would be congruent.  

In an isosceles trapezoid, the diagonals would also be congruent as base angles are equal and legs are equal.  When drawing diagonals this would create triangle congruences making the diagonals equal in length.

In a square, all 4 sides are equal, sides are also perpendicular, therefore by triangle congruencies the diagonals would be equal.

In a rhombus, the diagonals are NOT necessarily congruent.  One is longer than the other. (See image)

In the same image notice that the diagonals intersecting each other are also equal in length for each part bisected.

The diagonals in a rhombus bisect each other.  In the others, one might bisect another, but not each other

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