Formulas for determining one side, knowing the others and an angle ![]() The following properties apply when the isosceles trapezoid has an inscribed circumference (see figure 4 above):ġ7.- The diagonals intersect at right angles: AC ⊥ BDġ8.- The height measures the same as the median: HF = KL, that is, h = m.ġ9.- The square of the height is equal to the product of the bases: h 2 = BC⋅ADĢ0.- Under these specific conditions, the area of the trapezoid is equal to the square of the height or the product of the bases: Area = h 2 = BC⋅AD. If in an isosceles trapezoid the sum of the bases is equal to twice a lateral one, then the inscribed circumference exists. ∡BRA = ∡DRC = 90º Relations for isosceles trapezium with inscribed circumference If AK = KB and DL = LC ⇒ KL || AD and KL || BCĩ.- AM = MC = AC / 2 and DN = NB = DB / 2ġ0.- AO / OC = AD / BC and DO / OB = AD / BCġ3.- ∡DAB + ∡ABC = 180º and ∡CDA + ∡BCD = 180ºġ4.- If AD + BC = AB + DC ⇒ ∃ R than equidistant from AD, BC, AB and DCġ5.- If ∃ R equidistant from AD, BC, AB and DC, then:.Unique relationships of the isosceles trapeziumģ.- ∡DAB + ∡BCD = 180º and ∡CDA + ∡ABC = 180ºĦ.- A, B, C and D belong to the circumscribed circle. The following set of relationships and formulas refer to figure 3, where in addition to the isosceles trapezoid other important segments already mentioned are shown, such as diagonals, height and median. T scalene monkfish, which has all its different angles and sides.ġ2.- The segment that joins the midpoints of the diagonals has a length equal to the semi-difference of the bases.ġ3.- The angles adjacent to the lateral ones are supplementary.ġ4.- A trapezoid has an inscribed circumference if and only if the sum of its bases is equal to the sum of its sides.ġ5.- If a trapezoid has an inscribed circumference, then the angles with a vertex in the center of said circumference and sides that pass through the ends of the same side are right angles. Another important feature is the height, which is the distance that separates the parallel sides.īesides the isosceles trapezoid there are other types of trapezoid: In a trapezoid, the parallel sides are called bases and the non-parallels are called lateral. So this quadrilateral, or four-sided polygon, is in effect an isosceles trapezoid. Additionally, the angles ∠DAB and ∠ADC adjacent to the parallel side AD have the same measure α. In figure 1 we have the quadrilateral ABCD, in which the sides AD and BC are parallel. Examples of using the isosceles trapezoidĪ trapeze isoscelesis a quadrilateral in which two of the sides are parallel to each other and also, the two angles adjacent to one of those parallel sides have the same measure. ![]() -When you have the lateral, the median and an angle.-Know the diagonals and the angle they form with each other.-If the trapezoid can be inscribed a circumference. ![]()
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