CUBE is a parallelogram. CE is produced to T so that ET = EB and TB produced meets CU produced at Y. Prove that UY = UB.
Answers
Answer:
R.E.F image
Given : ABCD is A parallelogram
To Prove : BF=BC
Proof : In △DCE,DE=DC (given)
∴∠DCE=∠DEC...(1)
(Equal sides have equal is opposite to them)
since,
AB∥CD,∠DCE=∠BFC...(2) (pair of corresponding ∠S)
Form (1) and (2)
∠DEC=∠BFC
In △AEF,∠AEF=∠AFE
∴AF=AE,
⇒AB+BF=AD+DE
⇒BF=AD [∵AB=CD=DE]
⇒BF=BC [∵AD=BC] Hence proved.
Step-by-step explanation:
Eske jaisa hi question hai but Maine Sirf Parallelogram ke name alag alag liye.
Answer:
Refer to the attached figure.
Since, ABCD is a parallelogram, therefore AB is parallel to
CD.
Therefore, AF is parallel to CD.
And we can observe that EF is a traversal.
\angle 2 = \angle 4∠2=∠4 (Corresponding angles)
(Equation 1)
Therefore, AE is parallel to BC.
So, \angle 1 = \angle 3∠1=∠3 (Corresponding angles) (Equation 2)
Now, in triangle DEC,
DE = DC
Therefore,
So, \angle 1 = \angle 2∠1=∠2 (Equation 3)
(Angles opposite to the equal opposite sides are also
equal)
Therefore, \angle 3 = \angle 4∠3=∠4 (By equations 1,2 and 3)