Question

Prove that:
2. In the given figure (12.19), AD and BC bisect each other at point O.
(1) AB = CD andAC = BD
(ii) BCD = 2 CBA and DAC = ADB​

Answer 1

Step-by-step explanation:

AB and CD bisect each other at O i.e, AO=BO and CO=DO

in ΔCOA and ΔDOB

Given CO=OD,∠COA=∠BOD [ vertically opp angles]

AD=BD

∴ΔCOA≅ΔBOD

(i) ∴AC=BD[C.P.CT]

(ii) ∠CAB=∠ABD[C.P.CT]

again

in ΔCOB and ΔAOD

CO=OD [given]

BO=AO [given]

∠COB=∠AOD [vertically opp angles]

∴ΔCOB≅ΔAOD

∴∠CBA=∠BAD [ C.P. C.T]

(iii) and so AD∣∣CD [ ∵∠CBA=∠BAD which are altanate angles]

and AD=CB [C.P.C.T]

hope you understand it bro do hardwrok all the best

Answer 2

Step-by-step explanation:

Royal road: according to the Greek researcher Herodotus of Halicarnassus (fifth century BCE) the road that connected the capital of Lydia, Sardes, and the capitals of the Achaemenid Empire, Susa and Persepolis. ... Herodotus describes the road between Sardes and Susa in the following words.