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In the diagram, ABC is an isoscels triangle with the congruent sides and , and is the median drawn to the base . We know that ∠A ≅ ∠C, because the base angles of an isosceles triangle are congruent; we also know that ≅ , by definition of an isosceles triangle. A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. That means ≅ . This proves that ΔABD ≅ ΔCBD. Since corresponding parts of congruent triangles are congruent, that means ∠ABD≅ ∠CBD. Since the median is the common side of these adjacent angles, in fact bisects the vertex angle of the isosceles triangle.
What else can I help you with?
Can the altitude from the vertex angle of an isosceles triangle be the median?
If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.
A median of a triangle is a line or segment that passes through a vertex and bisects the side the vertex?
A median of a triangle is a line or segment that passes through a vertex and bisects the side of the triangle opposite the vertex.
Line segment with endpoints that are a vertex of a triangle and the midpoint of the side opposite the vertex?
median
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.
Is it possible for a segment to be a perpendicular bisector angle bisector median and altitude of a triangle?
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.
Do the medians of a triangle bisect the internal angles?
Not always. 1. The median to the base of an isosceles triangle bisects the vertex angle. 2. When the triangle is an equilateral triangle, then the medians bisect the interior angles of the triangle.
Does the altitude to the base of an isosceles triangle bisect the vertex angle?
bob
Can the altitude from the vertex angle of an isosceles triangle be the median?
If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.
A median of a triangle is a line or segment that passes through a vertex and the side opposite that vertex?
A median of a triangle is a line or segment that passes through a vertex and the midpoint of the side opposite that vertex. The median only bisects the vertex angle from which it is drawn when it is an isosceles triangle.
Does the angle bisector in a triangle bisect the opposite side?
Not necessarily. The only time that the angle bisector would bisect the opposite side is if you were bisecting the vertex angle of an isosceles triangle.
When is a median and an altitude the same segment?
In an isosceles or equilateral triangle, when from the vertex that is different from the others.
Is median is a angle bisector?
A median is a line drawn from the centre of a side of a triangle to the opposite vertex. Only in two cases does it also bisect the angle :- 1) All three medians of an equilateral triangle bisect the angle of the opposite vertex. 2) One median (from the unequal side to the enclosed angle of the two equal sides) bisects the angle of the opposite vertex.
Does a median divide a triangle into two congruent triangles?
Yes * * * * * No. A median is a line from a vertex to the midpoint of the opposite side. It divides the triangle into congruent parts only if the triangle is equilateral or if the triangle is isosceles and it is the median from the unequal vertex. In all other cases the two parts will not be congruent.
How many lines of symetry does isosceles triangle have?
Only one line of symmetry, it is the line that contains the median of the isosceles triangle (that passes through the vertex and perpendicular to the base).
What is a median of a triangle?
A median of a triangle is a line from a vertex of the triangle to the midpoint of the side opposite that vertex.
How is an isosceles trapezoid related to an isoceles triangle?
If the sloped sides of an isosceles trapezium are extended to a vertex, you would get an isosceles triangle.If the sloped sides of an isosceles trapezium are extended to a vertex, you would get an isosceles triangle.If the sloped sides of an isosceles trapezium are extended to a vertex, you would get an isosceles triangle.If the sloped sides of an isosceles trapezium are extended to a vertex, you would get an isosceles triangle.
A median of a triangle is a line or segment that passes through a vertex and bisects the side the vertex?
A median of a triangle is a line or segment that passes through a vertex and bisects the side of the triangle opposite the vertex.
