Draw a triangle ABC where AB = AC. Mark M as the midpoint of BC. Explain why AM is perpendicular to BC.
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Hey 邓万嗣, imagine a triangle that's perfectly balanced — two equal sides, like a seesaw with equal weights on both ends. [pause] There's a hidden line inside it that splits it into two perfect mirror images.
This is an isosceles triangle — AB and AC are exactly the same length. Draw a line from A down to the midpoint of the base, and something remarkable happens.
Many people think this line is just a nice decoration — a way to split the triangle in half. [pause] But actually, it's doing something far more precise.
Here's the key move. When you draw AM, you've created two smaller triangles — ABM and ACM. And because AB equals AC, and BM equals CM, these two are perfect twins.
Now here's the surprising part. [pause] Those two angles at M — the ones where AM meets the base — they must add up to 180 degrees because they form a straight line.
But since the two triangles are identical, those angles are equal to each other. Two equal angles that add to 180 — each one must be exactly 90 degrees.
And that's the whole idea, 邓万嗣. A 90-degree angle means perpendicular — so AM doesn't just split the base, it stands perfectly upright on it.