Name______Date______Class_____
Worksheet – Conditional Statements & Properties
Geometry
Write the converse, inverse, and contrapositive of each statement.
1. If water is frozen, then its temperature is below 0°C.
2. If x + 3 = 5, then x = 2.
3. If x is odd, then 3x is odd.
Decide whether the statement is true or false. If false, provide a counterexample.
4. The equation 4x – 3 = 12 + 2x has exactly one solution.
5. If x 2 = 36, then x must equal 18 or -18.
6. If mÐA = 122°, then the measure of the supplement of ÐA is 58°.
7. Two lines intersect in exactly one point.
Write the converse of each true statement. If the converse is also true, combine the statements to write a true biconditional statement.
8. If an angle measures 30°, then it is acute.
9. If two angles are supplementary, then their sum is 180°.
10. If an animal is a panther, then it lives in the forest.
Write each true statement in if-then form and write the converse. Determine the validity of each statement and write the biconditional (if possible).
11. Two perpendicular lines intersect to form four right angles.
12. A linear pair contains two supplementary angles.
13. Vertical angles are two non-adjacent angles.
14. Your friend claims the statement “If I bought a shirt, then I went to the mall” can be written as a true biconditional statement. Your sister says you cannot write it as a biconditional. Who is correct? Explain your reasoning.
15. Which statement has the same meaning as the given statement?
Given statement: You can watch a movie after you do your homework.
A) If you do not do your homework, then you can watch a movie afterward.
B) If you do your homework, then you can watch a movie afterward.
C) If you cannot watch a movie afterward, then do your homework.
D) If you can watch a movie afterward, then do not do your homework.
16. Can the statement “If x2-10=x+2, then x=4” be combined with its converse to form a true biconditional statement? Explain why or why not.
Use inductive reasoning to list the next two terms of the sequence.
17. Z, Y, X, W, V, … 18. J, F, M, A, M, …
19.
Algebra Review: Solve the literal equation for y.
20. 2y-2x=10 21. 20y+5x=15 22. 4y-5=4x+7
Algebra Review: Simplify.
23. 3-2x+2(x-1) 24. 1-(4x-6)+x