1. ## 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 .

2. I don't remember seeing an "m" before $\displaystyle \angle ABC$. 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.

3. Originally Posted by johny123
in statements why there is m symbol before angles like m<ABC + m<BCD=180
In axiomatic geometry courses it is written as $\displaystyle m\left( {\angle ABC} \right)$ because $\displaystyle m()$ is a function.
It is the function that measures angular size.
Different authors do use slightly different notations.

4. 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

5. 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 $\displaystyle m\angle ABC$ indicates the measure of an angle.
Whereas, the notation $\displaystyle \angle ABC$ stands for the angle itself: the union of two rays $\displaystyle \overrightarrow {BA} \cup \overrightarrow {BC}$.

6. 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 $\displaystyle m\angle ABC$ indicates the measure of an angle.
Whereas, the notation $\displaystyle \angle ABC$ stands for the angle itself: the union of two rays $\displaystyle \overrightarrow {BA} \cup \overrightarrow {BC}$.
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 ?

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

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

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

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