Is Satan shown lying in the bible?

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With Christ in his temptations he misrepresented Christ's authority to make bread out of stones durning his 40 day fast,

He tempts Christ into making stones to releive his hunger. Are you saying that Christ could NOT do such a thing?

he told Christ if he cast himself off the temple angels would catch him.

How is that a lie. Since Christ did no such thing then how do you know what would happen?

That if Christ bow down to him he would be allowed to rule the world.

Again how is that a lie?

Yes Christ could have made bread, but in doing so satan would have lead Christ in exceeding his fathers will.

So NOT a lie at all

In the second one satan was speaking for God. The problem satan did not know what God the Father would do.

Still no lie

The bowing down would meant satan would be in control of Christ and even if he turn the world over to Him satan would still be In control.

And not a lie either then