支【zhī】
1. prop up; put up; support 2. support 3. for long, thin things
[动]1、撑持,伸出,竖起 2、用物质或精神鼓励、帮助 [量]3、用于杆状的东西以及队伍、歌曲、乐曲等

他习惯用手支着头思考。
He has the habit of thinking with his head propped by hand.

看起来,他的确体力不支了。
It seems that he is worn out.

联欢会上,她唱了一支歌。
She sang a song in the party.
支撑【zhī chēng】
1. prop up; sustain; support 2. sustain; holdout; bear
[动]1、顶住物体使不倒塌 2、勉强维持

几根石柱支撑着那座小桥。
Several stone pillars support that small bridge.

由于生意清淡,这家店的营业收入只能支撑日常开销。
As the business is slack, the income of the shop can only sustain the daily expenditures.
支持【zhī chí】
1. sustain; holdout; bear 2. prop up; support
[动]1、勉强维持 2、给予鼓励或帮助

信念支持着长跑运动员跑完全程。
The faith sustained the long-distance runner to complete the race.

绿化工作得到了群众的热情支持。
Afforestation work has got enthusiastic support from the masses.