**Theorems dealing with Trapezoids and also Kites**

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**Terms that Use contact Person:**Donna Roberts

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

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

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

*Note:*The definition of one isosceles triangle states that the triangle has actually two congruent "sides". yet the meaning of isosceles trapezoid proclaimed above, mentions congruent basic "angles", not sides (or legs). Why?If one "inclusive" isosceles trapezoid is characterized to be "

*a trapezoid v congruent legs*", a parallelogram will certainly be an isosceles trapezoid. If this occurs, the various other properties that an isosceles trapezoid can possess can no much longer hold, because they will certainly not be true for a parallelogram.

If, however, we define an isosceles trapezoid to be a "

*trapezoid with congruent base angles*", the legs can be proven congruent, a parallelogram will certainly NOT be an isosceles trapezoid, and every one of the commonly known properties of one isosceles trapezoid will stay true.

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

THEOREM: If a square is a kite, it has one pair the opposite angle congruent.

THEOREM: If a square is a kite, it has actually one diagonal forming 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 of a quadrilateral is the perpendicular bisector that the other, the quadrilateral is a kite.

Topical summary | Geometry rundown | ubraintv-jp.com | MathBits" Teacher sources Terms that Use** call Person:** Donna Roberts