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See the diagram.
In ΔABC, draw MAPN which is any line through A. L is the midpoint of BC. Draw BM and CN both ⊥ to MAPN. Draw LP ⊥ MAPN.
In the trapezoid BMNC, as L is the midpoint of BC and LP || BM & CN, P will be the midpoint of MN.
Now consider the two triangles ΔLMP, and ΔLNP.
MP = PN. LP is a common side. m(∠P) = 90°.
So SAS criteria tells us that Δs LMP & LNP are congruent.
=> ML = NL.
Proved.
In ΔABC, draw MAPN which is any line through A. L is the midpoint of BC. Draw BM and CN both ⊥ to MAPN. Draw LP ⊥ MAPN.
In the trapezoid BMNC, as L is the midpoint of BC and LP || BM & CN, P will be the midpoint of MN.
Now consider the two triangles ΔLMP, and ΔLNP.
MP = PN. LP is a common side. m(∠P) = 90°.
So SAS criteria tells us that Δs LMP & LNP are congruent.
=> ML = NL.
Proved.
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Very nice
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