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Earn +20 ptsQ: Why is a line segment congruent to itself?
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A point that divides a line segment into two equal parts?
The midpoint divides a line segment into congruent parts.
A point on a line segment that divides the segment into two congruent segments?
The mid-point
What is a point that divides a line segment into two congruent segments?
It is its midpoint
What does it mean to bisect a line segment?
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.
Angle bisector of angleA of triangleABC is perpendicular to BC prove it is isosceles?
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.
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