2.1 Review Worksheet (continued)

23. Determine if the conjecture is valid by the Law of Detachment. Given: If one integer is odd and another integer is even, their product is even. The product of two integers is 24. Conjecture: One of the two integers is odd.

24. Determine if the conjecture is valid by the Law of Syllogism. Given: If an element is an alkali metal, then it reacts with water. If an element is in the first column of the periodic table, then it is an alkali metal. Conjecture: If an element is in the first column of the periodic table, then it reacts with water.

25. Draw a conclusion from the given information. Given: If Dakota watches the news, she is informed about current events.

If Dakota knows about current events, she gets better grades in Social Studies. Dakota watches the news.

2.1.4 Biconditional Statements and Definitions Write the conditional statement and converse within each biconditional. 26. Three points are coplanar if and only if they lie in the same plane.

27. A parallelogram is a rectangle if and only if it has four right angles.

28. A lunar eclipse occurs if and only if Earth is between the Sun and the Moon.

For each conditional, write the converse and a biconditional statement. 29. If today is Saturday or Sunday, then it is the weekend.

30. If Greg has the fastest time, then he wins the race.

31. If a triangle contains a right angle, then it is a right triangle.

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