Deductive geometry is a process of deriving geometric facts from previously-known facts by[br]using logical reasoning.[br][br][b]The Logical Form[/b][br]We use letters like P and Q to represent simple statements.[br]Premise 1: If P, then Q.[br]Premise 2: P is true.[br]Conclusion: Therefore, Q must be true.[br][br]If P, then Q can also be read as "P implies Q"[br]The notation is given as [math]P\longrightarrow Q[/math].[br][br]To make this easier to remember, replace the letters P and Q with actual events:[br][br]Example 1:[br][b]Statement P:[/b] It is raining.[br][b]Statement Q:[/b] The grass is wet.[br][br]The argument:[br]1. If it is raining (P), then the grass is wet (Q).[br]2. It is raining (P).[br]Conclusion: Therefore, the grass is wet (Q).[br][br][math]\therefore[/math]This is a valid argument.[br][br][br]Example 2:[br][b]Statement P:[/b] Dev lives in Johor Bahru.[br][b]Statement Q:[/b] Dev lives in Malaysia.[br][br]The argument:[br]1. If Dev lives in Johor Bahru, then he lives in Malaysia.[br]2. Dev lives in Malaysia.[br]Conclusion: Dev lives in Johor Bahru.[br][br]Even though the statement is true, it does not enable us to draw a valid conclusion about P.[br]If Dev lives in Malaysia, he might live in Johor Bahru. He could also live in Kuala Lumpur, or any other places in Malaysia.[br]These possibilities are counterexamples to disprove the validity of the argument.[br][math]\therefore[/math] This is an invalid argument.[br]Deductive reasoning is about reaching conclusions that must be true.[br][br][br]Example 3:[br][b]Statement P:[/b] [math]a^{^{\circ}}[/math] and [math]b^{^\circ}[/math] are corresponding angles.[br][b]Statement Q:[/b] [math]a^{^\circ}[/math] and [math]b^{^\circ}[/math] are equal.[br][br]The argument:[br]1. If [math]a^{^\circ}[/math] and [math]b^{^\circ}[/math] are corresponding angles, then they are equal.[br]2. [math]a^{^\circ}[/math] and [math]b^{^\circ}[/math] are corresponding angles.[br]Conclusion: [math]a^{^\circ}[/math] and [math]b^{^\circ}[/math] are equal.[br][br]This is a valid argument.[br][br][br]Now you try to make an argument related to geometry.