My roommate and i are having a house party. we invite 15 couples. at the party, everyone must shake hands with everyone whom they do not already know. at the end of the party, i can't remember the number of people i have met, so i go ask all other people at the party how many hands they have shaken, and they each tell me a different number. you do not shake hands with yourself or your 'partner' (the person with whom you came). how many hands did my roommate shake?

There are 105 handshakes that his roommate shake.

Step-by-step explanation:

Since we have given that

Number of couples = 15

As we know the "Handshaking lemma"

Here, n = 15

So, the number of handshakes would be

Hence, there are 105 handshakes that his roommate shake.

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.