Posted by chica on Thursday, November 18, 2010 at 10:15pm.
Complete the indirect proof.
Given: Rectangle JKLM has an area of 36 square centimeters. Side JK is at least 4 centimeters long.
Prove: KL<=9 centimeters
Geometry - MathMate, Friday, November 19, 2010 at 1:07pm
p: A=36 ∧ JK≥4
Indirect proof (by contradiction):
We try to establish:
i.e. if p is true, then q is true.
We will assume that p is true and q is false, i.e.
A=36, JK≥4, and that KL>9.
Let JK=4+x : x≥0, and
KL=9+y : y>0
Since y>0, so A>36
which cannot be true.
Therefore the assumption of
p and true and q is false is not valid (contradiction).
Therefore when p is true, q is true, or
if A=36, and JK≥4 then KL≤9.
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