Answer:
BC
Step-by-step explanation:
If altitude drawn from vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. Hence this altitude is also the angle bisector. – If median drawn from vertex A is also the angle bisector, the triangle is isosceles such that AB = AC and BC is the base.
An isosceles triangle is one with two equal-length sides. The altitude to the base of an isosceles triangle is also the median to the base.
An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
Assume an isosceles triangle ΔABC, as shown below with an altitude AD.
Now, in the two triangles formed ΔABD and ΔACD,
AD ≅ AD {Common side}
AB ≅ AC {Congruent sides of the isosceles ΔABC}
∠ABD ≅ ∠ADC {Conguent sides of an isosceles triangle}
Therefore, Using the SAS postulate the two triangles are said to be congruent triangles.
Further, as the two triangles are congruent, therefore, the length of the two sides BD and DC will be equal.
Since the median divides the triangle into two equal parts, the altitude AD has also divided the side BC into two equal parts.
Hence, the altitude to the base of an isosceles triangle is also the median to the base.
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