# a) Does the relation "is less than" have a transitive property b)\angle3 is acute while\angle4 is obtuse. State an inequality involving the measure of\angle3 and\angle4. c) Where points M and N are midpoints of AB and CD, respectively it is given that AM\congCN... State a conclusion regarding AB and CD.

a) Does the relation "is less than" have a transitive property?
b)$\mathrm{\angle }$3 is acute while $\mathrm{\angle }$4 is obtuse. State an inequality involving the measure of $\mathrm{\angle }$3 and $\mathrm{\angle }$4.
c) Where points M and N are midpoints of AB and CD, respectively it is given that AM $\cong$ CN... State a conclusion regarding AB and CD.
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Abraham Norris
(a) True,
Trastive property: let a,b,c be three numbers, if a < b & b < c then a < c
Therefore "is less than" [ < ] is a transtive property.
(b) True. Given $\mathrm{\angle }$3 is acute, implies $\mathrm{\angle }$3 < 900
and $\mathrm{\angle }$4 is obtuse, implies 900 < $\mathrm{\angle }$4
hence from trabstive property, $\mathrm{\angle }$3 < $\mathrm{\angle }$4
(c) Given M is midpoint of AB, Therefore AM = MB
and N is midpoint of CD, therefore CN = ND
Also, AM $\cong$ CN, hence MB $\cong$ ND
implies AB $\cong$ CD (since AM+MB = AB & CN+ND = CD)