the framework for a railroad bridge.. please answer
Answers
Given : framework for a railroad bridge.
ED∥ BC, AB∥ EF , PR ⊥ EB and m∠PER =130°.
To Find : Quadrilateral EPBR
∠P
∠EQP
Quadrilateral formed by join mid points of adjacent sides of a rectangle
Solution:
Opposite sides are parallel hence Parallelogram
also PR ⊥ EB , hence Diagonal are perpendicular to each other
so Quadrilateral EPBR is a rhombus
Sum of adjacent angle = 180° ( in a parallelogram / rhombus)
∠P + ∠PER = 180°
=> ∠P + 150° = 180°
=> ∠P = 30°
Diagonal of rhombus bisect each other perpendicularly.
∠EQP = 90°
Quadrilateral formed by join mid points of adjacent sides of a rectangle is RHOMBUS
as all sides are Equal to half of diagonal of original rectangle
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