Question

In the construction of the perpendicular bisector of a given line segment, as shown in the figure below trianglePBM congurent to trianglePMB by which congruence criterion?​

Answer 1

In the construction of the perpendicular bisector of a given line segment, as shown in the figure below triangle PBM congruent to triangle PMB.

From figure, we have,

Consider, in Δ PBM and Δ PMB

∠ P = ∠ P    ( common angle )

∠ B = ∠ B    ( common angle )

∠ M = ∠ M    ( common angle )

Using AAA theorem, we have,

∴ Δ PBM ≅ Δ PMB

Therefore, using AAA congruence criterion the triangle PBM congruent to triangle PMB.