Answer:
1. D
2. A
3. C
4. A
5. C
6. D
7. B
8. C
9. C
10. B
11. C
12. Look at explanation.
Step-by-step explanation:
1. Vertical angles are angles that are opposite each other. Complementary angles are equal to 90 degrees so D would be the answer.
2. The upside down carrot symbol represents an or.
3. The diagonals of a rhombus are perpendicular bisectors of each other but are not congruent. 10 is not prime because it has factors other than 1 and itself. Like 5 and 2.
4. You are changing the q statement negative, meaning it will not happen, but the p statement will happen so it stay positive. The triangle symbol without the bottom represents and leaving A as your only option.
5. A contrapositive statement is where you switch the hypothesis and the conclusion and then negate them both. So "If a number is a natural number, it is an integer" turns into "If a number is not and integer, then it is not a natural number."
6. Biconditional means that the statement is true when both parts of the statement have the same sign, meaning a positive or negative statement. By adding the not into both parts of the statement, you are making it negative but it still holds truth.
7. The converse of a statement is when you flip the parts of the sentence around.
8. Two pints can always be collinear because you can always draw a line through two points. Collinear means that you can draw a line through a said number of points and they all lay on that line.
9. If Mark goes on the boat he has to wear a life jacket and since then given is that he is on the boat, then he must have a life jacket on. All of the other statements may or may not happen but they are not guaranteed.
10. On Tuesdays Luke has math club so he will be on the late bus, that is a guarantee. But, Luke may take the late bus another day of the week so C doesn't work, we don't know if Luke has any other activities that cause him to take the late bus so D doesn't work, and Luke could have math club another day of the week so A doesn't work.
11. Since the circle representing square is inside the circle representing rectangle, the conclusion is a square can be a rectangle but a rectangle is not a square which is what the original statement is essentially saying.
12. Draw the three circles on another piece of paper and label them. She doesn't want to attend the trip so then get rid of the circle. Then shade the region where the prom and graduation overlap. Then add the graduation circle back in and erase any shading that is in the circle you drew for graduation.
