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More About A Perpendicular Proof
What is the hypothesis about point D in
"A Perpendicularity Proof"?
What is your conclusion?
You were trying to prove that:
Point D is on the perpendicular bisector of the segment connecting A and B (This
is your hypothesis)
The conclusion is...
So, putting the hypothesis
and your
conclusion together you will get:
If .....(hypothesis) , then ...
(conclusion).
Or
If ....(conclusion), then ... .(hypothesis). What does these statement means in term of Leslies' sprinkler dilemma from HW#2? Do you know what dilemma means? Then, don't just seat there go and figure it out. Why do you think that she has a dilemma? Did you notice that we were able to interchange the hypothesis and the conclusion to obtain two different ways of explaining our answer?
Learn this: If you can interchange one " If..., then...." true statement to form a second "If ..., then..." true statement, then each statement is called the converse of the other. You Try! Can you give the Converse statement of: Think: What are some real-life examples of "if...., then...." statements? One more thing" Mathematicians often use the phrase "If and only if" when they have two conditions where one true condition will guarantee that the other is also true. Example: D is equidistant from A and B if and only if D is on the perpendicular bisector of the segment connecting A and B.This statement is the equivalent of combining the two separate "If . . . , then . . . ." statements. Your knowledge in action. Use the "if ..., then...." statement to explain what does the Pythagorean Theorem say. Remember, the theorem only works with right triangle. Please let me know your answers. Here you can practice what you know. Happy As Mr. Lora Back to Orchard Hideout |
