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Why does the perpendicular bisector construction work?

This construction works by effectively building congruent triangles that result in right angles being formed at the midpoint of the line segment. The proof is surprisingly long for such a simple construction.

Why does a perpendicular bisector work?

The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. Each point on the perpendicular bisector is the same distance from each of the endpoints of the original line segment.

Why does the angle bisector construction work?

Constructing angle bisectors makes a line that gives two congruent angles for a given angle. For example, when an angle bisector is constructed for an angle of 70°, it divides the angle into two equal angles of 35° each. Angle bisectors can be constructed for an acute angle, obtuse angle, or a right angle too.

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Which is the correct construction for a perpendicular bisector?

A perpendicular bisector is a line that meets a given line segment at a right angle and cuts the given line segment into two equal halves. Constructing such a line requires that we draw an equilateral triangle on the given line segment and then bisect the third vertex.

What does perpendicular bisector mean?

Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

How is constructing a perpendicular bisector similar to constructing?

Constructing an angle bisector creates a line that bisects an angle, whereas constructing a perpendicular bisector creates a line that bisects a line segment. A line can then be drawn through the two points where the arcs intersect to create a perpendicular bisector.

Does the construction Demonstrate how do you bisect an angle correctly using technology?

Does the construction demonstrate how to bisect an angle correctly using technology? Yes; circles D and E have the same radius.

What are the steps in constructing perpendicular bisector?

The perpendicular bisector of a line segment

  1. open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.
  2. Call the two points where these two arcs meet C and D. Draw the line between C and D.
  3. CD is the perpendicular bisector of the line segment AB.
  4. Proof.

How is the perpendicular to a line constructed?

This page shows how to construct a perpendicular to a line through an external point, using only a compass and straightedge or ruler. It works by creating a line segment on the given line, then bisecting it. The bisector will be a right angles to the given line.

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When constructing a perpendicular bisector Why must the compass?

When constructing a perpendicular bisector Why must the compass opening be greater than the length of the segment? the reason that the compass opening has to be greater than 1/2 of the segment is so it can make arcs. and the arcs would have to cross in the middle so that when go to draw the line it would be straight.

When constructing a perpendicular bisector What angle will be formed?

‘Bisect’ is the term used to describe dividing equally. Perpendicular bisectors intersect the line segment that they bisect and make four angles of 90° each on both sides. Perpendicular means a line or a line segment making an angle of 90° with another line or line segment.

When constructing the perpendicular bisector of PQ What would be the correct first step?

1 Expert Answer The correct answer is A; the big arc must be drawn partly above segment PQ and partly below it. subsequently, the SAME big arc (i.e same radius) will be drawn with compass centered at Q.

When can you use the perpendicular bisector theorem?

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints. In other words, if we hanged laundry lines from any floor of our tower, each floor would use the same length of laundry line to reach the ground.

What is the difference between bisector and perpendicular bisector?

A (segment) bisector is any segment, line, or ray that splits another segment into two congruent parts. A perpendicular bisector is a special, more specific form of a segment bisector. In addition to splitting another segment into two equal parts, it also forms a right angle (90˚) with said segment.

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What is the perpendicular bisector equation?

⇒m1×m2=−1, where m2 is the slope of the perpendicular bisector. Perpendicular bisector will pass through the points A and B i.e. point M. In this case, the perpendicular bisector is eventually a line passing through point M(5,3) and having slope m2=1. Thus the equation of the perpendicular bisector is x−y−2=0.

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