ABCD is rectangle in which M is midpoint of BC. AM produced meets DC produced at E. Prove that CE=AB and BE= AC
Answers
Proved that CE=AB and BE= AC if Mid point of BC of ABCD rectangle prodced such that it meets produced DC at E
Step-by-step explanation:
M is mid point of BC
=> BM = CM = BC/2 = DA/2 ( as BC = DA , opposite sides equal in rectangle)
=> CM /DA = 1/2
CM ║ DA as M lies on CB & opposite sides of rectangle are parallel
=> Δ DAE ≈ Δ CME
=> DC/DE = AM/AE = CM/DA
=> DC/DE = AM/AE = 1/2
=> DE = 2 * DC AE = 2 AM
DE = DC + CE
=> DC + CE = 2 DC
=> DC = CE
DC = AB ( opposite sides of rectangle)
=> CE = AB
AC² = AB² + BC²
BE² = BC² + CE²
BE² = BC² + AB² (using CE = AB)
=> BE² = AB² + BC²
=> BE² = AC²
=> BE = AC
QED
Proved
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