SOLUTION: parallelogram abcd is a rhombus lmno are the midpoints.prove that the shape form inside rhombus is a rectangle.
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-> SOLUTION: parallelogram abcd is a rhombus lmno are the midpoints.prove that the shape form inside rhombus is a rectangle.
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I have labeled some angles with small letters: Here is just an outline
w + x = 180° (adjacent angles of a parallelogram are supplementary)
x + 2y = 180° (sum of interior angles of isosceles triangle BLM)
w + 2z = 180° (sum of interior angles of isosceles triangle CMN)
2y = 180° - x (solving for 2y)
2z = 180° - w (solving for 2z)
2y + 2z = 360° - x - w (adding the two preceding equations together)
2y + 2z = 360° - x - (180° - x) (substituting 180°-x for w from w + x = 180°
2y + 2z = 360° - x - 180° + x (removing parentheses)
2y + 2z = 180° (simplifying)
y + z = 90° (dividing through by 2)
y + z + angle LMN = 180° {they form a straight angle of 180°
90° + angle LMN = 180° (substituting 90° for y + z)
angle LMN = 90° (solving for angle LMN)
By the same way the other 3 angles of LMNO are 90°.
LMNO is a rectangle.
