Question

A quadrilateral which have three congruent triangle and four congruent triangle.​

Answer 1

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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