Hi Rita, It's not at all impolite to begin a conversation without one of these phrases, they're simply two of many options you have in English to begin a conversation or exchange. Some other options you have are: "How are you?", "What's up?"(informal), "What's going on?"(Also informal), "How's it going?", or even simply "Hello!" or "Hi". All perfectly acceptable and polite ways to initiate conversation. Since English doesn't have many rules or structures built into the words themselves to connote politeness we communicate politeness primarily with our tone of voice and facial expressions. For example, a "Hi!", said with a smile and rising intonation would communicate much more politeness and friendliness than a monotone, "How are you?" said with a blank expression. I'd like to note that these two phrases have specific uses as well-"How was your day?" and "How was your night?" are both used in specific contexts. We would usually use "How was your day?" with someone we're familiar with, like a friend, family member, or lover-someone you see on a regular basis. It's not very common to use among strangers since it implies that you really do want to hear about how someone's day was as opposed to being just a polite question. Same goes for "How was your night?", this would be used with people you're close with if you genuinely want to hear how their night was and isn't exactly something you'd approach a stranger with. Hope this helps! Michael