**Theorems dealing with Trapezoids and also Kites**

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The median of a trapezoid is a segment joining the midpoints that the foot of the trapezoid. (At the right, is the mean for trapezoid ABCD.) |

The theorems will be stated in "if ...then" form. Both the theorem and its converse (where friend swap the "if" and also "then" expressions) will be examined. Click in the charts below to view each proof.While one method of proof will certainly be shown, other techniques are also possible.

THEOREM: The typical of a trapezoid is parallel come the bases and half the sum of the lengths that the bases.

*Note:*The meaning of one isosceles triangle says that the triangle has actually two congruent "sides". however the meaning of isosceles trapezoid declared above, mentions congruent basic "angles", no sides (or legs). Why?If one "inclusive" isosceles trapezoid is defined to it is in "

*a trapezoid through congruent legs*", a parallelogram will be one isosceles trapezoid. If this occurs, the various other properties that an isosceles trapezoid have the right to possess can no longer hold, due to the fact that they will certainly not be true for a parallelogram.

If, however, we define an isosceles trapezoid to it is in a "

*trapezoid v congruent base angles*", the legs have the right to be proven congruent, a parallelogram will NOT be an isosceles trapezoid, and all of the commonly known properties of an isosceles trapezoid will stay true.

THEOREM: If a quadrilateral (with one set of parallel sides) is one isosceles trapezoid, its legs space congruent. THEOREM: (converse) If a trapezoid has its opposite angles supplementary, the is one isosceles trapezoid. You are watching: Diagonals of a trapezoid are congruent A dragon is a square whose four sides are attracted such that there space two distinctive sets the adjacent, congruent sides. DEFINITION: A kite is a quadrilateral whose 4 sides are drawn such that there are two distinctive sets of adjacent, congruent sides. |

THEOREM: If a square is a kite, it has actually one pair that opposite angles congruent.

THEOREM: If a quadrilateral is a kite, it has one diagonal developing two isosceles triangles.

THEOREM: If a quadrilateral is a kite, it has one diagonal forming two congruent triangles.

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THEOREM: If one of the diagonals that a quadrilateral is the perpendicular bisector of the other, the square is a kite.

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