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英語 高校生

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解決済み 回答数: 1
英語 高校生

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解決済み 回答数: 1
数学 高校生

(3)の解説を詳しくお願いします。解答で、なぜ2AM²=AC²+AB²-2BM²という式がたつのかがわかりません。

△ABCにおいて、辺BCの中点をMとし, AB=c, BC=2a, CA=6 とおくとき 0% (1) cos Bをa, b, c で表せ. (2) AM2をa,b,c で表せ. (3) AB²+AC²=2(AM²+BM²) が成りたつことを示せ. (1) △ABCに余弦定理を適用して cos B= 精講 (2) 三角形の内部に線が1本ひいてあると,1つの角を2度使うこ とができます.この問題でいえば, ∠B を △ABC の内角と考え て(1)を求め,次に △ABM の内角と考えて AM2 を求めることが それにあたります。 解答 - (3) この等式を中線定理 (パップスの定理)といいます. この等式は,まず使 5463 えるようになることが第1です. 使えるようになったら自力で証明すること を考えることも大切です.また,証明方法はこれ以外に,三平方の定理を使 う方法 (**)や数学ⅡIで学ぶ座標を使った方法,数学Cで学ぶベクトル CA を使う方法などがあります. DVD 図中の線分 AM を中線といいますが, この線分AM を 2:1に内分する 点Gを △ABC の重心といい (52) これから学ぶ数学ⅡIの「図形と方程 式」,数学Cの「ベクトル」 「複素数平面」でも再び登場します. 4a²+c2-62_4a²+c²-62 = C 2.2a.c 4ac (2) △ABM に余弦定理を適用して # B a - a AM²=c2+α²-2cacosB=c2+a- M a C 4a²+c²-6² 6²+c²-2a² 2 2 (3)a=BM,6=AC, c=AB だから, 2AM² = AC2 + AB2-2BM2 よって, AB2+AC2=2(AM²+BM² )

解決済み 回答数: 2