Theorems managing Trapezoids and also Kites mmsanotherstage2019.com Topical rundown | Geometry summary | MathBits" Teacher resources Terms that Use call Person: Donna Roberts

 The median of a trapezoid is a segment authorized the midpoints of the foot of the trapezoid. (At the right, is the median for trapezoid ABCD.)

The theorems will certainly be stated in "if ...then" form. Both the theorem and its converse (where you swap the "if" and "then" expressions) will certainly be examined. Click in the charts below to check out each proof.While one an approach of proof will certainly be shown, other techniques are likewise possible.

THEOREM: The median of a trapezoid is parallel come the bases and half the amount of the lengths of the bases.

Note: The meaning of one isosceles triangle states that the triangle has actually two congruent "sides". but the an interpretation of isosceles trapezoid declared above, mentions congruent base "angles", not sides (or legs). Why?If an "inclusive" isosceles trapezoid is characterized to it is in "a trapezoid through congruent legs", a parallelogram will be an isosceles trapezoid. If this occurs, the other properties the an isosceles trapezoid deserve to possess deserve to no longer hold, because they will certainly not be true for a parallelogram.
If, however, we specify 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 nature of one isosceles trapezoid will continue to be 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 actually its opposite angle supplementary, that is an isosceles trapezoid.You are watching: Are the diagonals of an isosceles trapezoid congruentA kite is a square whose four sides are drawn such that there room two unique sets of adjacent, congruent sides.DEFINITION: A kite is a quadrilateral whose 4 sides are attracted such that there room two distinct sets of adjacent, congruent sides.

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

THEOREM: If a quadrilateral is a kite, it has actually one diagonal creating 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 the the other, the square is a kite.

Topical summary | Geometry summary | mmsanotherstage2019.com | MathBits" Teacher sources Terms the Use call Person: Donna Roberts