dem·on·strate 
(dĕmən-strāt′)
(dĕmən-strāt′)v. dem·on·strat·ed, dem·on·strat·ing, dem·on·strates
v.tr.
1. To show clearly and deliberately; manifest: demonstrated her skill as a gymnast; demonstrate affection by hugging.
2. To show to be true by reasoning or adducing evidence; prove: demonstrate a proposition.
3. To present by experiments, examples, or practical application; explain and illustrate: demonstrated the laws of physics with laboratory equipment.
4. To show the use of (an article) to a prospective buyer: The salesperson plugged in and demonstrated the vacuum cleaner.
v.intr.
1. To give a demonstration: described the dance step, then took a partner and demonstrated.
2. To participate in a public display of opinion: demonstrated against tax hikes.
[Latin dēmōnstrāre, dēmōnstrāt- : dē-, completely; see DE- + mōnstrāre, to show (from mōnstrum, divine portent, from monēre, to warn; see men-1 in the Appendix of Indo-European roots).]