Why did France and Englan declare war on Germany when Germany's armies invaded Blegium?

You've asked this as a WWII question. In WWII France and Britain declared war on Germany when Germany invaded Poland. This was the latest aggressive move by the militaristic Germans, and the British and French were determined to try to stop Hitler before he took over all of Europe.

In WW ONE the British declared war on Germany when Germany invaded Belgium. The British were among four European Great Powers who had signed a Treaty in 1839 each pledging to perpetually respect and defend the neutrality of Belgium. Prussia had also signed this Treaty and Germany was a successor state to Prussia, the Prussian King was now the German Emperor, and Germany was still bound by its obligations under this Treaty.

In WW ONE the French went to war with Germany because the Germans attacked them. There was immediate fighting along the French-German border as Germans moved in. But this was merely a diversion. The main German attack was coming through Belgium, into the north of France. This was the reason the Germans invaded Belgium in the first place, to go through and get at northern France. This would allow the Germans to avoid the heavy forts and defenses the French had along their border with Germany.