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If two angle bisectors of a triangle are congruent then prove that triangle is isosceles?
Wiki User
∙ 15y ago
The two angle bisectors of a triangle are congruent the those two angles are congruent. The angles are bisected the same meaning that the whole and half angle are the same. For example if they are bisected at the whole angle 50 each, then each half is 25. The bisectors really don't mean anything and all you need is 50 to know it's isosceles. 50 and 50 is 100 and the left over for the last angle is 80 adding to 180. AND overall any 2 congruent angles in a triangle have the same congruent legs making it isosceles.
Wiki User
∙ 15y ago
If two angle bisectors of a triangle are congruent, then the triangle is isosceles. This is because the angle bisectors of a triangle are concurrent and the angle bisectors of a triangle that are congruent divide the opposite sides of the triangle into two equal segments. So if two angle bisectors are congruent, the sides opposite those angles are also equal, making the triangle isosceles.
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The intersection of the angle bisectors of a triangle?
The intersection of the angle bisectors of a triangle is called the incenter. It is equidistant from the sides of the triangle and can be constructed by drawing the angle bisectors of the triangle's angles. The incenter is the center of the incircle, which is the circle inscribed within the triangle.
The angle bisectors of a triangle share a common point of what?
The three bisectors meet at a point which is the centre of the circle. is you draw the circle that has that point as centre and 1 of the corners as a point on the circle, all corners will be on the circle
The orthocenter is the point shared by the angle bisector of a triangle?
Actually, the orthocenter of a triangle is the point where the three altitudes of the triangle intersect. The altitudes are perpendicular lines drawn from each vertex to the opposite side. The angle bisectors of a triangle intersect at the incenter, not the orthocenter.
Circles circumscribed about a given triangle will all have centers equal to the incenter but can have different radii?
Yes, that is correct. Circles circumscribed about a given triangle will have centers that are equal to the incenter, which is the point where the angle bisectors of the triangle intersect. However, the radii of these circles can vary depending on the triangle's size and shape.
Can equiangular triangles be acute?
Yes, equiangular triangles can be acute. An equiangular triangle is a triangle in which all three angles are equal. If all the angles are less than 90 degrees, the triangle is considered acute.
An angle not congruent to the base angles of an isosceles triangle?
The base angles of an isosceles triangle are congruent. The vertex angle of an isosceles triangle is not necessarily congruent to the base angles.
What are 2 properties of an isosceles triangle?
-- 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.
A triangle with two congruent sides and an angle of 104 degrees is?
A triangle with two congruent sides is isosceles. A triangle with an angle of 104 degrees is obtuse. So you would have an obtuse isosceles triangle.
Does the angle bisector of the vertex angle of an isosceles triangle divides the triangle into two congruent?
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.
How are perpendicular bisectors and angle bisectors the same?
In general, they are not. In an isosceles triangle, the perpendicular bisector of the base is the same as the bisector of the angle opposite the base. But the other two perp bisectors are not the same as the angle bisectors. Only in an equilateral triangle is each perp bisector the same as the angle bisector of the angle opposite.
If an angle bisector of an isosceles triangle yields two isosceles triangles what were the angle measures of the original triangle?
they would be congruent triangles!
What is an isosceles obtuse triangle?
An isosceles obtuse triangle is a triangle with 1 obtuse angle and only 2 congruent sides.
What is a triangle with a right angle and two congruent sides?
A right isosceles triangle.
What angle is congruent in an isosceles triangle?
The two "base" angles.
What is the vertex angle on an isosceles triangle?
the top angle the angle formed by the two congruent sides
What do you call a triangle with two congruent sides and an 145 degree angle?
An isosceles triangle
If An isosceles right triangle is a triangle with an angle measuring ninety degrees and no two sides congruent?
No. An isosceles right triangle has the measures of 90, 45, and 45. Isosceles means that two sides are congruent. Hope this helps :)
