Reflexive Property of Congruence
The midpoint divides a line segment into congruent parts.
The mid-point
It is its midpoint
Basically the definition of bisect is to separate two parts of a line segment to create two congruent line segments, which leads to them being equal.
Let D represent the point on BC where the bisector of A intersects BC. Because AD bisects angle A, angle BAD is congruent to CAD. Because AD is perpendicular to BC, angle ADB is congruent to ADC (both are right angles). The line segment is congruent to itself. By angle-side-angle (ASA), we know that triangle ADB is congruent to triangle ADC. Therefore line segment AB is congruent to AC, so triangle ABC is isosceles.
Congruent line segment
No, it is not true that a segment's bisector will always be congruent to the segment itself. A segment bisector is a line, ray, or segment that divides the original segment into two equal parts, but the bisector itself does not have to be equal in length to the original segment. For example, if you have a segment of length 10 units, its bisector will simply divide it into two segments of 5 units each, but the bisector itself can be of any length and orientation.
Line segment BC is congruent to Line Segment YZ
bisecting
congruent
No, they need not.
The line that divides a segment into two congruent segments is called the perpendicular bisector. This line intersects the segment at its midpoint and forms right angles with the segment, ensuring that the two resulting segments are equal in length.
It could be the diameter of a circle that produces 2 congruent segments or the midpoint of a line segment
The midpoint divides a line segment into congruent parts.
The mid-point
A bisector cuts a line SEGMENT into two congruent line segments. A line has indefinite or infinite length.
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