Congruence of Angles




Congruence of Angles:

Make a trace-copy of ∠ PQR. Try to superpose it on ∠ABC.
For this, first, place Q on B and QP along with BA.
Thus, ∠ PQR matches exactly with ∠ ABC.
That is, ∠ ABC and ∠ PQR are congruent.
We write ∠ ABC ≅ ∠ PQR or m∠ ABC =m∠ PQR...(In this case, the measure is 40°).

Now, you take a trace-copy of ∠ LMN. Try to superpose it on ∠ ABC.
Place M on B and `vec"ML"   "along" vec" BA"`.
No, in this case, it does not happen. You find that ∠ ABC and ∠ LMN do not cover each other exactly. So, they are not congruent.

Now, observe ∠XYZ and ∠ABC. The rays `vec" YX" and vec" YZ"`, respectively appear to be longer than `vec" BA" and vec" BC"`.
You may, hence, think that ∠ABC is smaller than ∠XYZ. But remember that the rays in the figure only indicate the direction and not any length. On superposition, you will find that these two angles are also congruent.

We write               ∠ABC ≅ ∠XYZ....................(ii)
or                        m∠ABC = m∠XYZ

In view of (i) and (ii), we may even write
∠ ABC ≅ ∠ PQR  ≅ ∠ XYZ

If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are the same.

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