Which of the following statements are true about a segment in a plane? Choose all that apply.
a. Every segment has infinitely many midpoints
b. Every segment has two bisectors
c. Every segment has one perpendicular bisector
d. Every segment has infinitely many congruent segments
e. Every segment has one line that is perpendicular to it
c. Every segment has one perpendicular bisector
d. Every segment has infinitely many congruent segments
e. Every segment has one line that is perpendicular to it
How is constructing an angle bisector similar to constructing a perpendicular bisector?
a. Both constructions begin with a given angle.
b. Both constructions require you to find the midpoint of a segment
c. Both constructions require that you draw a ray.
d. Both constructions require that you find the point where the two arcs intersect.
c. Both constructions require that you draw a ray.
thats not right
I apologize for the incorrect response. The correct answer is:
d. Both constructions require that you find the point where the two arcs intersect.
Constructing an angle bisector involves drawing two arcs from the vertex of the angle, while constructing a perpendicular bisector involves drawing two arcs with the same radius from the endpoints of the segment. In both cases, the point where the two arcs intersect is used to construct the bisector.
Given <A, how can you construct an angle whose measure is 1/4m<A?
To construct an angle that has a measure of one-fourth the measure of angle A, you can follow these steps:
1. Place the compass at the vertex of angle A and draw an arc that intersects both rays of the angle.
2. Without changing the compass width, place the compass at one of the points where the arc intersects one of the rays of angle A. Draw an arc that intersects the other ray of angle A.
3. Place the compass at the vertex of the angle again and set the compass width to the distance between the intersection point on one ray and the vertex.
4. Without changing the compass width, place the compass at the intersection point on the other ray and draw an arc that intersects the first arc drawn in step 2.
5. Using a straightedge, draw a line connecting the vertex of angle A to the intersection point of the two arcs.
The resulting line will be the angle bisector that divides angle A into two smaller angles, one of which has a measure of one-fourth the measure of angle A.
Which of the statements is false?
a. There are infinitely many lines parallel to a given line
b. There are infinitely many perpendicular to a given line
c. There are infinitely many perpendicular bisectors of a given segment.
d. There are infinitely many segments that are congruent to a given segment
b. There are infinitely many perpendicular to a given line.
This statement is false. In Euclidean geometry, there is only one line that is perpendicular to a given line at a specific point. If a line is perpendicular to another line, it will only intersect at one point of intersection.