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Mathematics Senior High

14でどうして→と←どっちの場合も証明が必要ですか?解答のどちらかを証明したら⇔のどっちも成り立つことにならないんですか?

14 ■指針■ 四角形 ABCD が平行四辺形であることから, ベクトルに関してどのような関係式が成り立 つかを考える。 A B を証明するときは, A⇒BとBAの両方を証明する。 ⇒ の証明) 四角形 ABCD が平行 四辺形であるとき AC=AB+AD 1 また B BD = 10411 よって AC+BD=(AB+AD)+(AD-AB) =AD-AB =2AD ←の証明) AC+ BD=2AD を変形して AC-AD=AD-BD よって DC=AD+DB すなわち DC AB したがって, DC//AB, DC = ABであるから, 四角形 ABCD は平行四辺形である。 -15) (D) S D 15 (1) (3,-1)=(x,y) よって Find Pat よって x-3=5-x, 4=y+1)=(8) これを解いてx=4,y=4 x=3, y=-13 (2) (x-3,4)=(5-x,y) € =(3, -6)+(-3, 2)=(3-3, -6+2) =(0, -4) (6) -2a-36=-2(1,-2)-3(-3,2) 18 sa+tb=s(4, 2) + (-3, 5) = (4s-3t,2s+5t) =(-2, 4)+(9, -6) =(-2+9, 4-6)=(7, -2) (1) c = sato とすると JA (5, 9)=(4s-3t, 2s+5t) よって 4s-3t=5, 2s+5t=9 これを解くと s = 2, t=1 したがって c=2a+b (2) d=sa + to とすると (10, -8)=(4s-3t, 2s+5t) よって 4s-3t=10, 2s+5t=-8 これを解くと s=1, t=-2 したがって d=a-2b (3) = sa + to とすると したがって BUC FARCIE □ 14 四角形ABCD について,次のことを証明せよ。 (-3, 6)=(4s-3t, 2s+5t) A SOA よって 4s-3t= -3, 2s+5t = 6 これを解くと 3 15 26 13 S=- JA t= 58 四角形 ABCD が平行四辺形である ⇔ AC+BD=2AD =OA f=a+ -34+158 88 26 HAR MA 19 (100であるから, // になるの は、 = ka となる実数 k が存在するときである。

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English Senior High

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4 eehaupbsorl elstog 空欄にあてはまるものを (A)~(D) の中から選んで記号を書きましょう。 rinom soon tundA (8) 1. My first of Toronto was very positive. (A) impressed (B) impressing (C)impressive (D) impression swdua vd oo visuay 1 (5) 3. 2. The special equipment was (A) originally (B) origin (C) original (D) originality 4. The manufacturer (A) produces vaboj alriemriserter prind soinom bib vilW..t A teacher's class. Sum ob incinu vertone (A) friendship (B) friendlily (C) friendly (D) friendliness Autoledad blow approach makes new students feel comfortable in their new es new students fee (B) has produced shwob trand enirkham y 5. It is necessary that the applicant 8. Would you mind (A) open made for those who have mobility problems. mismo2( bloo out a'fariT (8) Of(0) tripim men (8) TV sets in developing countries ten years ago. (D) has been produced (C) produced (A) fill (B) filled (C) fills (D) would fill 6. Tomoko invited me to see the musical with (A) she (C) (B) heraners 10. Is there anyone (A)whom blueWF Tesy jasi cio 7. The CEO by the charity foundation to speak at their annual conference, but he had to decline the request because of a scheduling conflict. (A) asked (D) had been asking (B) was asked (C) has asked 9. The meeting will be held (A) in dar out the form before the job interview. toy bollit need cen (A) admun orong olidam ym e'evgH (8) Jeneves need even ment (2) eldabil opening prupiolansi (B) whose blow reiwi at sol no (D) herself them. the window for me? vietne.m (C) to open (D) to be opening Houp (0) (B) on (C) for (D) at nismen (0) Meason (2) gribnstalue (8) 10:30 in the conference room. is against this alternative proposal? (D) which m) boysin .GP .er Deda briced OS eldialval (A) 11. Tim is as as Linda. (A) more intelligent (B) intelligent (C) less intelligent (D) better intelligent for storage. (A) designated (B) detained (C) reciprocated (D) signified 12. According to the proposal, a large block of rooms in the east wing of the new building will be

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English Senior High

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4 eehaupbsorl elstog 空欄にあてはまるものを (A)~(D) の中から選んで記号を書きましょう。 rinom soon tundA (8) 1. My first of Toronto was very positive. (A) impressed (B) impressing (C)impressive (D) impression swdua vd oo visuay 1 (5) 3. 2. The special equipment was (A) originally (B) origin (C) original (D) originality 4. The manufacturer (A) produces vaboj alriemriserter prind soinom bib vilW..t A teacher's class. Sum ob incinu vertone (A) friendship (B) friendlily (C) friendly (D) friendliness Autoledad blow approach makes new students feel comfortable in their new es new students fee (B) has produced shwob trand enirkham y 5. It is necessary that the applicant 8. Would you mind (A) open made for those who have mobility problems. mismo2( bloo out a'fariT (8) Of(0) tripim men (8) TV sets in developing countries ten years ago. (D) has been produced (C) produced (A) fill (B) filled (C) fills (D) would fill 6. Tomoko invited me to see the musical with (A) she (C) (B) heraners 10. Is there anyone (A)whom blueWF Tesy jasi cio 7. The CEO by the charity foundation to speak at their annual conference, but he had to decline the request because of a scheduling conflict. (A) asked (D) had been asking (B) was asked (C) has asked 9. The meeting will be held (A) in dar out the form before the job interview. toy bollit need cen (A) admun orong olidam ym e'evgH (8) Jeneves need even ment (2) eldabil opening prupiolansi (B) whose blow reiwi at sol no (D) herself them. the window for me? vietne.m (C) to open (D) to be opening Houp (0) (B) on (C) for (D) at nismen (0) Meason (2) gribnstalue (8) 10:30 in the conference room. is against this alternative proposal? (D) which m) boysin .GP .er Deda briced OS eldialval (A) 11. Tim is as as Linda. (A) more intelligent (B) intelligent (C) less intelligent (D) better intelligent for storage. (A) designated (B) detained (C) reciprocated (D) signified 12. According to the proposal, a large block of rooms in the east wing of the new building will be

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