Question

The perpendicular bisectors of AABC intersect at point G. Find the length of BG. B

Answer 1

Answer:

$\overline{GB}$ = 9

Step-by-step explanation:

The given parameters are;

The point of intersection of the perpendicular bisectors of the sides $\overline{BC}$, $\overline{BA}$, and $\overline{CA}$ intersect (meet) at point G

Let D represent the point of intersection of the perpendicular bisector from G to $\overline{BC}$, we have for ΔBGD and ΔCGD;

$\overline{GD}$ ≅ $\overline{GD}$ by reflexive property

∠GDB = ∠GDC = 90° given that $\overline{GD}$ is the perpendicular bisector of $\overline{BC}$

Similarly, $\overline{DB}$ ≅ $\overline{DC}$, also given that  $\overline{GD}$ is the perpendicular bisector of $\overline{BC}$

Therefore;

ΔBGD ≅ ΔCGD by Side-Angle-Side (SAS) rule of congruency

$\overline{GB}$ ≅ $\overline{GC}$   by Congruent Parts of Congruent Triangles are Congruent, (CPCTC)

$\overline{GB}$ = $\overline{GC}$ = 9 by definition of congruency

∴ $\overline{GB}$ = 9.