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Q: What triangle has an altitude which is also a median and angle bisector?

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It's in the definition of an angle bisector: An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.and an isoceles triangle:it is a triangle with (at least) two equal sides. This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

Label the triangle ABC. Draw the bisector of angle A to meet BC at D. Then in triangles ABD and ACD, angle ABD = angle ACD (equiangular triangle) angle BAD = angle CAD (AD is angle bisector) so angle ADB = angle ACD (third angle of triangles). Also AD is common. So, by ASA, triangle ABD is congruent to triangle ACD and therefore AB = AC. By drawing the bisector of angle B, it can be shown that AB = BC. Therefore, AB = BC = AC ie the triangle is equilateral.

-- An isosceles triangle has two equal sides. -- An isosceles triangle has two equal angles. -- An isosceles triangle has two equal interior-angle bisectors. -- The bisector of the vertex angle of an isosceles triangle is also the perpendicular bisector of the triangle's base.

No, the angle bisector of a scalene triangle actually intersects at two points, the point between the two points and the vertex formed by two lines of a scalene triangle. * * * * * On an alternative interpretation of the question, the three angle bisectors of any triangle always intersect at a point which is called the incentre.

There are a lot of videos and applets out there that explain how to construct an angle bisector.

Related questions

The altitude is the segment from an angle of a triangle to the side opposite of the angle which is intersected perpendicularly by the altitude., the angle bisector cuts an angle into two congruent angles, and a median forms two congruent line segments.

No, it's not true.

No. The angle bisector is a line. Where the three lines meet is the median. In an equilateral triangle the INTERSECTION of the angle bisectors is the median.

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.

If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.

Yes. The bisector of one angle of a triangle is the perpendicular bisector of theopposite side if the bisected angle is the vertex angle of an isosceles triangle,or any angle of an equilateral triangle.

Yes.

Yes. In an isosceles or equilateral triangle, it always is.

It's in the definition of an angle bisector: An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.and an isoceles triangle:it is a triangle with (at least) two equal sides. This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

Yes - the altitude of an equilateral triangle is perpendicular to the side chosen as the base and bisects that side and the opposite angle. Also, the altitude of an isosceles triangle when measured from the third side (the side that is not equal to the other two sides) is a perpendicular bisector of the base and also bisects the opposite angle.

Yes, provided that the base is not one of the 2 equal sides. And it's also the perpendicular bisector of the base.

triangles angle bisector is called incenter..

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