# when constructing a perpendicular bisector why must the arcs intersect

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## When constructing an angle bisector, why must the arcs intersect?

The arcs must intersect in order to connect to the vertex of the angle.

When constructing an angle bisector, we open our compass to any width, and place the point of the compass on the vertex of the angle. We then construct an arc through both sides of the angle.

Next we move the compass to the point where our constructed arc intersects one side of the angle. We then draw an arc inside of the angle.

Using the compass set to the same width, we move the compass to the point where our first arc intersects the other side of the angle, drawing an arc inside of the angle. This new arc will intersect our previous arc, creating a point.

We then use a straightedge to connect this point to the vertex of the angle, giving us our bisector.

If the two arcs did not intersect, we would not have a point to connect to the vertex.

## Perpendicular Bisector Properties

Perpendicular bisectors can bisect a line segment or a line or the sides of a triangle. The important properties of a perpendicular bisector are listed below.

Perpendicular bisector,

- Divides a line segment or a line into two congruent segments.
- Divides the sides of a triangle into congruent parts.
- They make an angle of 90Â° with the line that is being bisected.
- They intersect the line segment exactly at its midpoint.
- The point of intersection of the perpendicular bisectors in a triangle is called its circumcenter.
- In anÂ acute triangle, they meet inside a triangle, in an obtuse triangle they meet outside the triangle, and inÂ right triangles, they meet at theÂ hypotenuse.
- Any point on the perpendicular bisector isÂ equidistantÂ from both the ends of the segment that they bisect.
- Can be only one in number for a given line segment.

**Important Notes on Perpendicular Bisector**

- A perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.
- The perpendicular bisector of a triangle is considered to be a line segment that bisects the sides of a triangle and is perpendicular to the sides.
- Perpendicular bisector on a line segment can be constructed easily using a ruler and a compass.

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### How do you draw a perpendicular bisector?

Drawing perpendicular bisector for a line: Place the sharp end of a pair of compasses at one end of the line, and open it to just over half of the line. Draw an arc which must intersect the line in the position described. Then put the sharp end at the other of the line and, keeping the compassing at the same length, draw another arc which intersects the first one twice and also the line. Then draw a straight line through the two places where the arcs intersect. This line is the perpendicular bisector.

Drawing perpendicular bisector of angle: Places the sharp end of the compass at the point of the angle and, after having opened it arbitraily wide, draw an arc which intersects the two lines meeting to form the angle each once in the said position. Then remove the compass and, always keeping it opened at the SAME length, place the sharp end at each of the two places where the previous arc cuts each of the two lines meeting to form the angle. In this position with the described length, draw a small arc at each of the said places, which should cross each other. Draw a straight line from the point of the angle to this crossing. This should be the bisector of the angle.

### The measure of a tangent-tangent angle is half the difference of the measures of the intercepted arcs?

True

### How do you find midpoint of a segment?

Take a compass, extend it about 3/4 of the length of the segment. Then from one end of the segment, draw a 180 degree arc. From the other end draw another arc. Connect the points where the arcs intersect. Where the line intersects with the segment is the midpoint of the segment. That is how you bisect a segment to find the midpoint – geometrically.

### Measures of minor arcs equal measures of inscribed angles?

lol. your on odyssey ware

### How do you draw a spherical triangle where the sum of the angles is 190 degrees?

You could draw two arcs from the North pole to the equator, with a 10 degree separation. The two arcs and the equator would form a 190 degree spherical triangle.

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