2.3 Biconditionals and 2.4 Law of Detachment / Syllogism
Name: __________________
1. Complete the following statement: A conditional statement can be rewritten as a biconditional if………….
2. Can the following statement be written as a biconditional statement? If so, rewrite the statement as a
biconditional statement.
If two angles are vertical angles, then the angles are congruent.
3. Can the following statement be written as a biconditional statement? If so, rewrite the statement as a
biconditional statement.
If a number is an even number, then the number is divisible by 2.
4. Use the Law of Detachment / Syllogism to make a conclusion based on the information provided. If no
conclusion can be made, write NO CONCLUSION and Explain WHY!
If an angle is a right angle, then it is not acute.
mQ is equal to 90.
5. Use the Law of Detachment / Syllogism to make a conclusion based on the information provided. If no
conclusion can be made, write NO CONCLUSION and Explain WHY!
If two angle measures sum to 180, then the angles are supplementary
If two angle measures sum to 90, then the angles are complementary
6. Use the Law of Detachment / Syllogism to make a conclusion based on the information provided. If no
conclusion can be made, write NO CONCLUSION and Explain WHY!
If you live in Santa Monica, you live in California. If you live in California, you live on the West Coast.
Cheryl lives in Santa Monica
7. What are the conclusions that you can make from the following statement?
Segment AB and Segment RD have the same lengths.
Segment RD is twice as long as Segment WE.
Segment WE has a length of 32 centimeters.
8. Given the conditional statement, write the converse, inverse, and contrapositive. Also provide the truth
value for all 4 conditional and related statements.
If two angles are right angles, then the two angles are congruent.