Yes, it is true.
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.
thank goodness for my math teacher, norm! he said only in an isosceles triangle. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base! =)
a line or segment that is perpendicular to the given segment and divides it into two congruent segments
Yes. If you have an isosceles triangle standing up on the unequal side, thenthe line segment from the top vertex perpendicular to the base is all of these.
It splits one side of the triangle into two congruent parts.
That will depend on what type of triangle it is as for example if it is an isosceles triangle then it will form two congruent right angle triangles.
they would be congruent triangles!
Every isosceles or equilateral triangle.
A "perpendicular bisector" is a line. There are no triangles of any kind in a line.
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.
thank goodness for my math teacher, norm! he said only in an isosceles triangle. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base! =)
A perpendicular bisector splits a line segment into two congruent parts.
Equilateral triangles
equilateral triangles
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.
Similarities between angle bisector and perpendicular bisector: Perpendicular bisector bisects a line segment into two equal parts at 90°. Angle bisector bisects an creating two congruent angles they both bisect into equal parts! =)
True