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skad [1K]
2 years ago
13

Given:

Mathematics
1 answer:
notsponge [240]2 years ago
3 0

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

BD ⊥ AC (given)

BD = 3 units, and AC = 8 units.

BD is the <em>perpendicular</em> bisector of <u>segment</u> AC (given)

Thus,

<BDA  ≅ <BDC <em>(right</em> angles formed by a <u>perpendicular</u> bisector)

AD ≅ DC <em>(equal</em> parts of a<em> bisected l</em>ine)

AD ≅ DC = 4 units

Thus joining <u>points</u> B to A, and B to C,

BA ≅ BC.

So that applying <em>Pythagoras</em> 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 <u>concluded</u> that point D is <em>equidistant</em> from points A and C.

For more clarifications on a perpendicular bisector of a line, visit: brainly.com/question/929137

#SPJ1

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Complete proof is written below.

Facts and explanation about the segments shown in question :

  1. As BC = EF is a given statement in the question
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<em />

<em>STATEMENT                              REASON  </em>

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1. BC = EF                                    1. Given

2. AB + BC = AC                         2. Betweenness

3. AC > BC                                   3. Def. of segment inequality

4. AC > EF                                   4. Def. of congruent segments

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<em>Keywords: statement, length, reason, proof</em>

<em> Learn more about proof from brainly.com/question/13005321</em>

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