a) Does the relation "is less than" have a transitive property?b) ∠3 is acute while ∠4 is obtuse. State an inequality involving the measure of ∠3 and ∠4.c) Where points M and N are midpoints of AB and CD, respectively it is given that AM ≅ CN... State a conclusion regarding AB and CD.

Question

a) Does the relation &quot;is less than&quot; have a transitive property?b)  ∠3 is acute while   ∠4 is obtuse. State an inequality involving the measure of   ∠3 and   ∠4.c) Where points M and N are midpoints of AB and CD, respectively it is given that AM   ≅ CN... State a conclusion regarding AB and CD.

Abraham Norris · Accepted Answer

(a) True,Trastive property: let a,b,c be three numbers, if a &amp;lt; b &amp;amp; b &amp;lt; c then a &amp;lt; cTherefore &quot;is less than&quot; [ &amp;lt; ] is a transtive property.(b) True. Given   ∠3 is acute, implies   ∠3 &amp;lt; 900and   ∠4 is obtuse, implies 900 &amp;lt;   ∠4hence from trabstive property,   ∠3 &amp;lt;   ∠4(c) Given M is midpoint of AB, Therefore AM = MBand N is midpoint of CD, therefore CN = NDAlso, AM   ≅ CN, hence MB   ≅ NDimplies AB   ≅ CD (since AM+MB = AB &amp;amp; CN+ND = CD)

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