HONG KONG — A Hong Kong police officer on Tuesday shot a teenage demonstrator, the first time in months of protests that a live round was fired at a protester. The shooting capped an evening of violent protests, escalating the territory’s political crisis on the same day that the central government staged a huge military parade in Beijing to celebrate 70 years of Communist control.

The protesters in Hong Kong hoped to upstage Beijing’s celebrations by holding their own unauthorized marches. Violence quickly broke out, as demonstrators in districts across the city engaged in some of the bloodiest and most sustained clashes since protesters began taking to the streets in early June.

The split screen — pageantry in Beijing versus violence, tear gas and street fires in a restive Chinese territory — was hardly the image that China’s top leader, Xi Jinping, had hoped to show the world.

The protester was shot in the Tsuen Wan district of northern Hong Kong. Tsuen Wan is a working-class area near Hong Kong’s border with the Chinese mainland, miles from the city’s gleaming financial district.