Track / Stage 4 / 161 of 340 #421 of 2000

Problem 421

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

If $(\mathrm{AB}) // (\mathrm{CD}), (\mathrm{AB}) \perp (\mathrm{EF})$ and finally $(\mathrm{EF}) \perp (\mathrm{GH})$ .

What can be said about $(\mathrm{CD})$ and $(\mathrm{GH})$ ?

Your answer

Official solution

(EF) $\perp$ (GH) and (EF) $\perp$ (AB)

Therefore (GH) // (AB)

Or (AB) // (CD)

Therefore (CD) // (GH)

Some of these reasonings are more computational, in these cases, we use arrows:

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.