agantisbz

2022-07-27

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.

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.

Abraham Norris

Beginner2022-07-28Added 16 answers

(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)

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)

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