Erik is bisecting a segment with technology. Which of the following describes his next step?
1 answer:
Answer: Choice (3). Draw a circle with center A and radius equal to CB.
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Explanation:
Your teacher wasn't clear with this, but I'm assuming the distance from B to C is greater than half of AB. Otherwise, the bisection wouldn't be possible.
Assuming this is the case, drawing a circle centered at A with the same radius, will allow us to intersect the two circles at points D and E as shown below. Segment DE is the perpendicular bisector of AB. We can prove this through the use of congruent triangles. Segment DE cuts AB into two smaller equal pieces FA and FB, so FA = FB.
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It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
<h3>How to prove a Line Segment?</h3>We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Read more about Line segment at; brainly.com/question/2437195
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