agantisbz

## Answered question

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.

### Answer & Explanation

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)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?