in the adjoining figure ABCD is a parallelogram. through the midpoint M of the side CD, a line is drawn which cuts diagonal AC produced at E . prove that EL=2BL
Answers
Hence proved, EL=2BL
Step-by-step explanation:
Solution given below
Proved that EL = 2BL.
Given
To prove that, EL = 2BL.
From the figure,
M is the mid-point of CD.
In ΔBMC and ΔEMD, MC = MD.
∠CMD = ∠EMD ( They are vertically opposite angles )
∠MBC = ∠MED ( They are alternate angles )
Hence, ΔBMC = ΔEMD ( AAS - Angle Angle Side congruence )
Where, ABCD is a parallelogram
BC = DE ---> ( 1 )
AD = BC ---> ( 2 )
Adding them, AD + DE = BC + BC
AE = 2 BC ( AD + DE = AE )
AE = 2 BC ---> ( 3 )
In ΔAEL and ΔCBL,
∠ALE = ∠CLB ( They are vertically opposite angles )
∠EAL = ∠BCL ( They are alternate angles )
Δ AEL ≅ ΔCBL ( By AA - Angle Angle similarity )
EL / BL = AE / BC
EL / BL = 2BC / BC ( AE = 2BC )
EL / BL = 2
EL = 2BL
Therefore, it has been proved that EL = 2BL.
To learn more...
1. brainly.in/question/618927
2. brainly.in/question/1538939
