Why we put m sign in demonstrative geometry in theorem?

**johny123** · March 3rd 2011, 12:11 AM

Why we put m sign in demonstrative geometry in theorem?
please tell me while proving theorems
in statements why there is m symbol before angles like m<ABC + m<BCD=180
thanks .

**emakarov** · March 3rd 2011, 01:29 AM

I don't remember seeing an "m" before $\angle ABC$ . My guess would be that it stands for "measure", i.e., the magnitude of the angle as opposed to the angle itself as a geometric figure.

**Plato** · March 3rd 2011, 02:43 AM

Originally Posted by johny123

Why we put m sign in demonstrative geometry in theorem?
in statements why there is m symbol before angles like m<ABC + m<BCD=180

In axiomatic geometry courses it is written as $m\left( {\angle ABC} \right)$ because $m()$ is a function.
It is the function that measures angular size.
Different authors do use slightly different notations.

**johny123** · March 3rd 2011, 02:56 AM

i am in 9th standard , i have seen m symbol before angles but i am confused when/where to put this symbol while proving. please define it .i have my exam in couple of days.

else i gotta cram all my theorems b4 exam. :P

**Plato** · March 3rd 2011, 03:08 AM

Originally Posted by johny123

i am in 9th standard , i have seen m symbol before angles but i am confused when/where to put this symbol while proving. please define it .i have my exam in couple of days.

As I said above, that is a matter determined by the author of your text material. Consult your textbook.
All one can say is that in general $m\angle ABC$ indicates the measure of an angle.
Whereas, the notation $\angle ABC$ stands for the angle itself: the union of two rays $\overrightarrow {BA} \cup \overrightarrow {BC}$ .

**johny123** · March 3rd 2011, 03:24 AM

Originally Posted by Plato

As I said above, that is a matter determined by the author of your text material. Consult your textbook.
All one can say is that in general $m\angle ABC$ indicates the measure of an angle.
Whereas, the notation $\angle ABC$ stands for the angle itself: the union of two rays $\overrightarrow {BA} \cup \overrightarrow {BC}$ .

Ok one confusion remains ,i have noticed that m symol is everywhere in the statements , but the author put it where there is equal sign(=) like sum of angles e.g m<ABC + m<BCD=90 here is m , where there is congruency of anlges there is no 'm' sign e.g <ABC=~ <BCD (=~ is for congrueny ) :-) so now could please define y is 'm' sign here ?

**Plato** · March 3rd 2011, 03:37 AM

Originally Posted by johny123

where there is congruency of anlges there is no 'm' sign e.g <ABC=~ <BCD (=~ is for congrueny ) :-) so now could please define y is 'm' sign here ?

If we have $m\left( {\angle ABC} \right) = m\left( {\angle BCA} \right)$ then it follows that $\angle ABC \cong \angle BCA$ , they are congruent.

It is incorrect to write $m\angle ABC \cong m\angle BCA$

**emakarov** · March 3rd 2011, 07:28 AM

To add, when we take a sum of two angles, we must use $m$ to convert angles as figures to numbers first and then to add the results. That's why $m$ is used in $m\angle ABC + m\angle BCD=90$ . To say that two angles are congruent, we don't need $m$ since we could say $\angle ABC\cong \angle BCD$ . The latter fact is equivalent to $m\angle ABC = m\angle BCD$ .

**johny123** · March 3rd 2011, 08:39 PM

Now i got this concept .Thanks Plato and Emakarov for your nice explanation :-)

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