Does a ps3 play ps2 games?

i just upgraded from an old crt tv to a lcd hdtv. ps2 games look like crap on it. i did some research and found that by using a component cable (the kind with 5 connectors) it would improve the quality quite a bit. sadly my tv doesnt have the connections for it. i figure i could upgrade to a ps3, which ive... show more i just upgraded from an old crt tv to a lcd hdtv. ps2 games look like crap on it.

i did some research and found that by using a component cable (the kind with 5 connectors) it would improve the quality quite a bit. sadly my tv doesnt have the connections for it.

i figure i could upgrade to a ps3, which ive heard connects with a HDMI cable (can anyone confirm this?) which my tv does have a port for.

will a ps3 play ps2 games? most of my ps2 games do have a progressive scan option, which ive heard makes them look tons better on a hdtv, and can be the difference between playable and unplayable. composite cables, which im using now dont allow for it.
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