The saying 'count on your partner for one trick' applies not only when you're trying to make a point, but also when you're trying to euchre your opponents. An example would be a hand in which your team takes the first or second trick and you still hold the right (giving you two sure tricks). You still need a little help from your partner, so be sure to give them the chance. It may be the only way to successfully euchre your opponents.
The dealer is in the East position. Bidding gets passed back and he places the 10 of clubs in his hand.
South starts off the hand by leading the 10 of hearts. West and North follow suit. The dealer/maker(E) takes the trick with the 10 of clubs (trump).
Next the maker(E) leads the ace of diamonds. South trumps in with the 9. West and North seats follow suit.
South is now thinking about a euchre. It would be a fair guess the maker(E) has three trump since they picked-up without holding the right. Leading the right here may only serve to help them by making their hand stronger. So South plays the 9 of spades. The hope is that their partner(N) can take this trick. North tries, but the maker(E) takes the trick away from him with the ace of trump.
Now the maker(E) leads the king of diamonds. South knows the only chance they have for a euchre is if their partner(N) can get this trick. Only three trump have been played and the partner(N) played a trump queen on the last diamond lead. Maybe North has one of the remaining trump. South gives their partner a chance and throws off the 10 of spades. Yes, their partner(N) had a trump and was able to take the trick. This makes the euchre complete.
Go back and see how the hand would have turned out if South, after taken the second trick had played the right. This would have pulled their partner's trump thus removing the one chance for them to help. This would have assured the maker of a point. It is the difference of three points in the score.
With most hands you will need your partner's help; if not, you should be playing alone.
Allowing your partner the opportunity to take a trick is often the difference between winning and losing. Remember, the points tend to go to the team utilizing the most effective techniques.