The altitude and median of an isosceles triangle _________.

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Coincide

Are collinear

Are non-collinear

Are different

answer is A.

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Detailed Solution

Consider an isosceles triangle $△ A B C$ .
Question Image

We know that a line that is drawn perpendicularly from one vertex of a triangle to the opposite side is defined as the altitude of a triangle.

The median of a triangle is a line segment that bisects one side by connecting a vertex to the opposing side's midway.

Draw the median and altitude of an isosceles triangle.

Let us draw a line segment AL that is perpendicular to BC, then AL is an altitude for this $△ ABC$ _.

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same.

We can see that the length of BL and LC is also the same.

Therefore, AL is a median of this triangle as well.

Therefore, AL is altitude and also the median of $△ ABC$ , this suggests that it coincides.

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