Geometry Section 2.2 Conditional Statements

Vocab

Conditional Statement

If and then statements

Hypothesis

Part after “if” independent

Conclusion

Part after “then” dependent

Biconditional 

Works both ways

Truth Value

T+T=T or T+F=F

Type	Definition	Form	Trick	Truth Value Rule	Example
Original (Conditional)	A statement that says if one thing happens, another will follow.	If H, then C	—	—	If it rains, then the ground gets wet.

Converse	Switch the hypothesis and the conclusion.	If C, then H	Switch	❌ Not always same truth value	If the ground gets wet, then it rains.

	Inverse Negate both the hypothesis and the conclusion. If not H, then not C Negate ❌ Not always same truth value If it doesn’t rain, then the ground doesn’t get wet.
		nverse Negate both the hypothesis and the conclusion. If not H, then not C Negate ❌ Not always same truth value If it doesn’t rain, then the ground doesn’t get wet.
		nverse Negate both the hypothesis and the conclusion. If not H, then not C Negate ❌ Not always same truth value If it doesn’t rain, then the ground doesn’t get wet.

Contrapositive

Switch and negate both the hypothesis and conclusion.

If not C, then not H

Switch + Negate

✅ Always same truth value as the original

If the ground isn’t wet, then it didn’t rain.

• Original ↔ c

• Contrapositive → same truth values

• Converse ↔

Inverse → same truth values