Question

ABCD is a rhombus.BA is produced to O where BA=AO.Prove that the angle ODB is a right angle​

Answer 1

Answer:Given : ABCD is a rhombus AB produced to E and F such that AE=AB=BF.

Construction : Join ED and CF and produce it to meet at G,  

To : ED⊥FC prove  

proof : AB is produced to points E and F such that  

AE=AB=BF __(i)

Also since ABCD is a rhombus

AB=CD=BC=AD __(ii)

Now in ΔBCF,BC=BF [from (i) & (ii)]

1!=2!

3!=1!+2! [exterior angle]

3!=22! __(iii)

Similarly , AE=ED

5!=6!

4!=5!+6!=25!         5!+2!+E!GF=180  

o

 

4!=25!__(iv)             E!GF=90  

o

 

by adding (iii) and (iv)

4!+3!=25!+22!               ∴4! and 3! are consective interior angles

∴EG⊥FC Now in ΔEGF   Hence it proved

Step-by-step explanation: