please tell this answer quickly
Answers
AE = AD , DE bisects ∠ADC & ∠DEC = 90° if CE bisects ∠BCD and E is midpoint of AB
Step-by-step explanation:
As AB ║ CD
=> ∠ECD = ∠CEB ( alternate angle)
CE bisects ∠BCD
=> ∠BCE = ∠ECD
from Both
∠CEB = ∠BCE
=> BE = BC
BE = AE ( as E is mid point of AB)
BE = AD ( opposite sides of Parallelogram)
from both
=> AE = AD
as AE = AD
=> ∠ADE = ∠AED
∠AED = ∠CDE ( alternate angle)
=> ∠ADE = ∠CDE
=> DE bisects ∠ADC
in a parallelogram sum of adjacent angles = 180°
=> ∠ADC + ∠BCD = 180°
=> 2∠CDE + 2∠DCE = 180°
=> ∠CDE + ∠DCE = 90°
while in Δ DCE
∠CDE + ∠DCE + ∠DEC = 180°
=> 90° + ∠DEC = 180°
=> ∠DEC = 90°
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