Question

Given:

Answer 1

A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points  A and C.

BD ⊥ AC (given)

BD = 3 units, and AC = 8 units.

BD is the perpendicular bisector of segment AC (given)

Thus,

<BDA  ≅ <BDC (right angles formed by a perpendicular bisector)

AD ≅ DC (equal parts of a bisected line)

AD ≅ DC = 4 units

Thus joining points B to A, and B to C,

BA ≅ BC.

So that applying Pythagoras theorem to ΔABD, we have:

$/hyp/^{2}$ = $Adj 1^{2}$ + $Adj 2^{2}$

$AB^{2}$ = $3^{2}$ + $4^{2}$

       = $\sqrt{25}$

 AB      = 5 units

So that,

BA ≅ BC = 5 units

Therefore, it can be concluded that point D is equidistant from points A and C.

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