A quadrilateral which have three congruent triangle and four congruent triangle.
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A quadrilateral which have three congruent triangle and four congruent triangle.
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Answer:
In the above image, I've drawn 2 different quadrilaterals with 3 equal sides & 4th side // one of the 3 sides
Draw AB = AD = BC or BE =r, & AB //DC ( ie we get ABCD an isosceles trapezoid OR we get ABED , a rhombus parallelogram), proof given below
Or Draw AB = BC = AD or AF =r, & AB // DC ( ie we get ABCD an isosceles trapezoid or we get ABCF , a rhombus parallelogram), proof given below
XY // X'Y'
<ABE = <CEB = x …………… (1)
Tri OBA ~ Tri OEF
=> OB/OE = OA/OF
=> (OB/OE) + 1 = (OA/OF) + 1
=> BE/OE = AF/OF
=> r/ OE = r/OF
=> OE = OF
=> <EFO = x …………….. (2)
=> <ADC = <BCE = x ………… (3)
=> ABCD is an isosceles trapezoid ••
Since DC//XY
=> <DAX = x …………. (4)
=> < DAB = DEB ( as both are supplement to x )
=> ABED is a parallelogram ( as both the pairs of opposite angles are equal)
Since all sides of this parallelogram are equal. Hence it is a rhombus••
[Proved]
Step-by-step explanation:
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