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Theorems managing Trapezoids and Kites bsci-ch.org Topical outline | Geometry outline | MathBits" Teacher sources Terms of Use call Person: Donna Roberts
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The median the a trapezoid is a segment involvement the midpoints the the foot of the trapezoid. (At the right,
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is the median for trapezoid ABCD.)
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The theorems will be declared in "if ...then" form. Both the theorem and also its converse (where you swap the "if" and also "then" expressions) will be examined. Click in the charts listed below to view each proof.While one method of proof will certainly be shown, other methods are also possible.


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THEOREM: The typical of a trapezoid is parallel to the bases and fifty percent the amount of the lengths that the bases.
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Note: The definition of an isosceles triangle says that the triangle has two congruent "sides". however the definition of isosceles trapezoid declared above, mentions congruent basic "angles", not sides (or legs). Why?If an "inclusive" isosceles trapezoid is identified to be "a trapezoid with congruent legs", a parallelogram will certainly be one isosceles trapezoid. If this occurs, the various other properties the an isosceles trapezoid can possess deserve to no much longer hold, since they will not be true for a parallelogram.
If, however, we define an isosceles trapezoid to it is in a "trapezoid through congruent base angles", the legs have the right to be proven congruent, a parallelogram will NOT it is in an isosceles trapezoid, and all of the typically known properties of one isosceles trapezoid will stay true.

THEOREM: If a square (with one collection of parallel sides) is an isosceles trapezoid, the legs room congruent.
THEOREM: (converse) If a trapezoid has its opposite angle supplementary, that is one isosceles trapezoid.

You are watching: An isosceles trapezoid is a trapezoid with congruent legs


A kite is a quadrilateral whose four sides are drawn such the there room two unique sets the adjacent, congruent sides.
DEFINITION: A kite is a square whose four sides are attracted such the there are two unique sets that adjacent, congruent sides.
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THEOREM: If a quadrilateral is a kite, it has one pair of opposite angle congruent.

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

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THEOREM: If a square is a kite, it has actually one diagonal creating two congruent triangles.

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THEOREM: If among the diagonals the a square is the perpendicular bisector the the other, the square is a kite.


Topical rundown | Geometry outline | bsci-ch.org | MathBits" Teacher sources Terms the Use call Person: Donna Roberts