6-2: Indirect Proofs Proof Geometry.

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6-2: Indirect Proofs Proof Geometry

Indirect proofs (proof by contradiction) Indirect proofs work by: Assuming the opposite of what you are trying to prove. Draw logical conclusions based on this assumption. Come to a CONTRADICTION of a known fact. Since your conclusions were valid, your assumption must be FALSE

Example Conjecture: It is not raining. (statement to be proved) Proof: Suppose It was raining. (supposition) Then the people coming in the door would be wet. (conclusion resulting from supposition) But they are dry. (the CONTRADICTION) So It MUST not be raining.

Now you try! Conjecture: Today is not a snow day Suppose Today is a snow day. (supposition) Then there would be no one at school. (conclusion resulting from supposition) But We are all here. (the CONTRADICTION) So It MUST not be a snow day.

Indirect proof video

Let’s talk math: Indirect Proof example Δ𝐴𝐵𝐶 𝑖𝑠 𝑠𝑐𝑎𝑙𝑒𝑛𝑒, 𝐵𝐷 ⊥ 𝐴𝐶 Conjecture: 𝐵𝐷 is not the median. Suppose: (supposition) Then: (conclusion resulting from supposition) But: (the CONTRADICTION) So:

You try! Given: 𝑆𝑄 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑃𝑆𝑅, 𝑚∠𝑃𝑄𝑆≠𝑚∠𝑅𝑄𝑆 Prove: 𝑃𝑆≠𝑅𝑆

You try! A B C D

Homework HW: pg 179 #1-3, 5-8, 11