平行線と角
2026年10月5日
最終更新日時 :
2026年10月7日
futaba_Agent
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"grade": "中学2年",
"field": "平行と合同",
"unit": "平行線と角",
"level": "標準",
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"front": {
"title": "平行なら同位角と錯角が等しい",
"text": "図のABとEFは平行です。直線CDが横切ると、∠BOCと∠FPOは同位角なので等しくなります。\n∠AOPと∠FPOは錯角なので、この二つも等しくなります。∠BOC=60°なら∠FPO=60°です。",
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"text": "AB∥EF、∠BOC=50°です。∠FPOは{blank:1}°、使った性質は{blank:2}です。",
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"title": "等しい角から平行を示す",
"text": "ABとEFが平行かまだ分からないとき、∠BOCと∠FPOがどちらも60°と分かったとします。\n同位角が等しければAB∥EFと判断できます。錯角が等しい場合も平行です。平行を仮定して角を求める向きとは逆です。",
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"text": "△ABCの∠B=50°、∠C=60°とします。三角形の三つの内角の和は180°です。\n∠Aを除く二角の和は$50+60=110$°。残りは$180-110=70$°です。",
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"title": "三つの内角を180°から求める",
"text": "△ABCの∠B=45°、∠C=65°です。二角の和は{blank:1}°、∠Aは{blank:2}°です。",
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"text": "△ABCでBCをCの先へ延長した外角を考えます。外角と∠Cの和は180°です。\n三角形の内角和も180°なので、外角は∠Aと∠Bの和になります。∠A=70°、∠B=50°なら外角は120°です。",
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"295°",
"57.5°"
],
"hint": "二直線の間にある錯角を探します。",
"explanation": "平行線の錯角は等しいので115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
},
{
"id": "A",
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},
{
"id": "B",
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},
{
"id": "C",
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{
"id": "D",
"x": 161.96768923394984,
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{
"id": "P",
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"y": 115,
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},
{
"id": "E",
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}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "7",
"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=35°、∠C=65°です。∠Aを選びなさい。",
"choices": [
"80°",
"100°",
"145°",
"115°"
],
"hint": "三つの角の和は180°です。",
"explanation": "180−35−65=80より80°。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 130.46279835657236,
"y": 151.6572666631831,
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"vertex": "B",
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"radius": 16
},
{
"vertex": "C",
"from": "B",
"to": "A",
"label": "65°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "8",
"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=55°、∠C=75°です。∠Aを選びなさい。",
"choices": [
"50°",
"130°",
"125°",
"105°"
],
"hint": "三つの角の和は180°です。",
"explanation": "180−55−75=50より50°。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 126.78853529174793,
"y": 91.05312631502255,
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{
"vertex": "C",
"from": "B",
"to": "A",
"label": "75°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "9",
"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=40°、∠C=85°です。∠Aを選びなさい。",
"choices": [
"55°",
"125°",
"140°",
"95°"
],
"hint": "三つの角の和は180°です。",
"explanation": "180−40−85=55より55°。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 151.79307940080668,
"y": 121.19446830661074,
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"label": "40°",
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"reflex": false,
"radius": 16
},
{
"vertex": "C",
"from": "B",
"to": "A",
"label": "85°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "10",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=45°、∠B=70°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"135°",
"25°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は45+70=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 92.6045899940537,
"y": 70.47007683166896,
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"y": 215,
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{
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"y": 215,
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"id": "D",
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],
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"A",
"B",
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] }
],
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"vertex": "A",
"from": "C",
"to": "B",
"label": "45°",
"rightAngle": false,
"reflex": false,
"radius": 16
},
{
"vertex": "B",
"from": "A",
"to": "C",
"label": "70°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "11",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=55°、∠B=60°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"125°",
"5°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は55+60=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 106.38385096065832,
"y": 100.01979733405979,
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"x": 40,
"y": 215,
"showLabel": true
},
{
"id": "C",
"x": 160,
"y": 215,
"showLabel": true
},
{
"id": "D",
"x": 240,
"y": 169.1435697769302
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],
"segments": [
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}
],
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"A",
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"C"
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{
"vertex": "A",
"from": "C",
"to": "B",
"label": "55°",
"rightAngle": false,
"reflex": false,
"radius": 16
},
{
"vertex": "B",
"from": "A",
"to": "C",
"label": "60°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "12",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=35°、∠B=80°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"145°",
"45°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は35+80=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 66.44904710626976,
"y": 65.0,
"showLabel": true
},
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"y": 215,
"showLabel": true
},
{
"id": "C",
"x": 136.39519582951954,
"y": 215,
"showLabel": true
},
{
"id": "D",
"x": 240,
"y": 252.85318053754162
}
],
"segments": [
{
"from": "C",
"to": "D"
}
],
"polygons": [
{
"points": [
"A",
"B",
"C"
] }
],
"labels": [],
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"angleMarks": [
{
"vertex": "A",
"from": "C",
"to": "B",
"label": "35°",
"rightAngle": false,
"reflex": false,
"radius": 16
},
{
"vertex": "B",
"from": "A",
"to": "C",
"label": "80°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "13",
"type": "choice",
"label": "平行の判定",
"question": "図で∠BOC=∠FPOと分かりました。AB∥EFといえる根拠を選びなさい。",
"choices": [
"同位角が等しいから",
"対頂角が等しいから",
"隣角の和が180°だから",
"図で同じ向きに見えるから"
],
"hint": "異なる交点の、同じ位置にある角です。",
"explanation": "同位角の等しさは二直線が平行になる条件です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
},
{
"id": "A",
"x": 30,
"y": 70,
"showLabel": true
},
{
"id": "B",
"x": 245,
"y": 70,
"showLabel": true
},
{
"id": "C",
"x": 145.98076211353316,
"y": 25,
"showLabel": true
},
{
"id": "D",
"x": 68.03847577293367,
"y": 160,
"showLabel": true
},
{
"id": "P",
"x": 94.01923788646684,
"y": 115,
"showLabel": true
},
{
"id": "E",
"x": 30,
"y": 115,
"showLabel": true
},
{
"id": "F",
"x": 245,
"y": 115,
"showLabel": true
}
],
"segments": [
{
"from": "A",
"to": "B"
},
{
"from": "C",
"to": "D"
},
{
"from": "E",
"to": "F"
}
],
"polygons": [],
"labels": [],
"segmentMarks": [],
"angleMarks": [],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "14",
"type": "choice",
"label": "性質と条件",
"question": "「二直線の錯角が等しければ二直線は平行」の仮定を選びなさい。",
"choices": [
"錯角が等しい",
"二直線が平行",
"対頂角が等しい",
"三角形の内角和が180°"
],
"hint": "「〜ならば」の前が与えられた条件です。",
"explanation": "錯角の等しさを仮定し、平行を結論にしています。"
},
{
"id": "15",
"type": "choice",
"label": "内角と外角",
"question": "三角形の内角が125°の頂点の、隣り合う外角を選びなさい。",
"choices": [
"55°",
"125°",
"235°",
"180°"
],
"hint": "内角と隣の外角で一直線になります。",
"explanation": "180−125=55°です。"
}
] }
"meta": {
"subjectId": "math",
"grade": "中学2年",
"field": "平行と合同",
"unit": "平行線と角",
"level": "標準",
"drillId": "math-2d002a"
},
"cards": [
{
"id": "1",
"front": {
"title": "平行なら同位角と錯角が等しい",
"text": "図のABとEFは平行です。直線CDが横切ると、∠BOCと∠FPOは同位角なので等しくなります。\n∠AOPと∠FPOは錯角なので、この二つも等しくなります。∠BOC=60°なら∠FPO=60°です。",
"visual": {
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"points": [
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"id": "O",
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"y": 70,
"showLabel": true
},
{
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{
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"showLabel": true
},
{
"id": "C",
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"y": 25,
"showLabel": true
},
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"showLabel": true
},
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}
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"alt": "本文の点・辺・角に対応する図。"
}
},
"back": {
"title": "平行なら同位角と錯角が等しい",
"text": "AB∥EF、∠BOC=50°です。∠FPOは{blank:1}°、使った性質は{blank:2}です。",
"answers": [
"50",
"平行線の同位角は等しい"
],
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
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"id": "D",
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"id": "P",
"x": 82.2405165970224,
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}
],
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}
}
},
{
"id": "2",
"front": {
"title": "等しい角から平行を示す",
"text": "ABとEFが平行かまだ分からないとき、∠BOCと∠FPOがどちらも60°と分かったとします。\n同位角が等しければAB∥EFと判断できます。錯角が等しい場合も平行です。平行を仮定して角を求める向きとは逆です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
},
{
"id": "A",
"x": 30,
"y": 70,
"showLabel": true
},
{
"id": "B",
"x": 245,
"y": 70,
"showLabel": true
},
{
"id": "C",
"x": 145.98076211353316,
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"showLabel": true
},
{
"id": "D",
"x": 68.03847577293367,
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},
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},
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"id": "E",
"x": 30,
"y": 115,
"showLabel": true
},
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"id": "F",
"x": 245,
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"alt": "本文の点・辺・角に対応する図。"
}
},
"back": {
"title": "等しい角から平行を示す",
"text": "∠AOP=∠FPOです。この二つは{blank:1}なので、ABとEFは{blank:2}と判断できます。",
"answers": [
"錯角",
"平行"
],
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
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"showLabel": true
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{
"id": "B",
"x": 245,
"y": 70,
"showLabel": true
},
{
"id": "C",
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"x": 30,
"y": 115,
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"x": 245,
"y": 115,
"showLabel": true
}
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}
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}
}
},
{
"id": "3",
"front": {
"title": "三つの内角を180°から求める",
"text": "△ABCの∠B=50°、∠C=60°とします。三角形の三つの内角の和は180°です。\n∠Aを除く二角の和は$50+60=110$°。残りは$180-110=70$°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 111.08755185424573,
"y": 130.28115468897548,
"showLabel": true
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{
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{
"id": "C",
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}
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{
"points": [
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"C"
] }
],
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{
"vertex": "B",
"from": "A",
"to": "C",
"label": "50°",
"rightAngle": false,
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"radius": 16
},
{
"vertex": "C",
"from": "B",
"to": "A",
"label": "60°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
"back": {
"title": "三つの内角を180°から求める",
"text": "△ABCの∠B=45°、∠C=65°です。二角の和は{blank:1}°、∠Aは{blank:2}°です。",
"answers": [
"110",
"70"
],
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 121.83821405597216,
"y": 133.16178594402786,
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{
"id": "B",
"x": 40,
"y": 215,
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{
"id": "C",
"x": 160,
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"C"
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"vertex": "B",
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"to": "C",
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{
"vertex": "C",
"from": "B",
"to": "A",
"label": "65°",
"rightAngle": false,
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"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
}
},
{
"id": "4",
"front": {
"title": "外角は離れた二つの内角の和",
"text": "△ABCでBCをCの先へ延長した外角を考えます。外角と∠Cの和は180°です。\n三角形の内角和も180°なので、外角は∠Aと∠Bの和になります。∠A=70°、∠B=50°なら外角は120°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 111.08755185424573,
"y": 130.28115468897548,
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{
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"y": 215,
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}
},
"back": {
"title": "外角は離れた二つの内角の和",
"text": "△ABCで∠A=40°、∠B=75°。BCをCの先へ延ばす外角は{blank:1}で{blank:2}°です。",
"answers": [
"$40+75$",
"115"
],
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 80.1923788646684,
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}
}
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"questions": [
{
"id": "1",
"type": "choice",
"label": "平行線の同位角",
"question": "AB∥EF、∠BOC=35°です。∠FPOを選びなさい。",
"choices": [
"35°",
"145°",
"215°",
"17.5°"
],
"hint": "平行線の同位角を対応させます。",
"explanation": "同位角なので35°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
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{
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"id": "B",
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"y": 25,
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{
"id": "D",
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"y": 160,
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{
"id": "P",
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"y": 115,
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"vertex": "O",
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}
},
{
"id": "2",
"type": "choice",
"label": "平行線の錯角",
"question": "AB∥EF、∠FPO=35°です。∠AOPを選びなさい。",
"choices": [
"35°",
"145°",
"215°",
"17.5°"
],
"hint": "二直線の間にある錯角を探します。",
"explanation": "平行線の錯角は等しいので35°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
},
{
"id": "A",
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{
"id": "B",
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"id": "D",
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"id": "P",
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}
},
{
"id": "3",
"type": "choice",
"label": "平行線の同位角",
"question": "AB∥EF、∠BOC=65°です。∠FPOを選びなさい。",
"choices": [
"65°",
"115°",
"245°",
"32.5°"
],
"hint": "平行線の同位角を対応させます。",
"explanation": "同位角なので65°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
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{
"id": "A",
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"id": "B",
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},
{
"id": "4",
"type": "choice",
"label": "平行線の錯角",
"question": "AB∥EF、∠FPO=65°です。∠AOPを選びなさい。",
"choices": [
"65°",
"115°",
"245°",
"32.5°"
],
"hint": "二直線の間にある錯角を探します。",
"explanation": "平行線の錯角は等しいので65°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
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"id": "5",
"type": "choice",
"label": "平行線の同位角",
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"choices": [
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"295°",
"57.5°"
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"hint": "平行線の同位角を対応させます。",
"explanation": "同位角なので115°です。",
"visual": {
"kind": "geometry",
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"id": "O",
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},
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"65°",
"295°",
"57.5°"
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"points": [
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"id": "O",
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},
{
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"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=35°、∠C=65°です。∠Aを選びなさい。",
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"100°",
"145°",
"115°"
],
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"explanation": "180−35−65=80より80°。",
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"points": [
{
"id": "A",
"x": 130.46279835657236,
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"vertex": "C",
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"radius": 16
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}
},
{
"id": "8",
"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=55°、∠C=75°です。∠Aを選びなさい。",
"choices": [
"50°",
"130°",
"125°",
"105°"
],
"hint": "三つの角の和は180°です。",
"explanation": "180−55−75=50より50°。",
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"points": [
{
"id": "A",
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{
"vertex": "C",
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"radius": 16
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},
{
"id": "9",
"type": "choice",
"label": "三角形の内角",
"question": "△ABCで∠B=40°、∠C=85°です。∠Aを選びなさい。",
"choices": [
"55°",
"125°",
"140°",
"95°"
],
"hint": "三つの角の和は180°です。",
"explanation": "180−40−85=55より55°。",
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"id": "A",
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"vertex": "C",
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"to": "A",
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"radius": 16
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},
{
"id": "10",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=45°、∠B=70°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"135°",
"25°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は45+70=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
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"id": "C",
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"y": 215,
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"id": "D",
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],
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"vertex": "B",
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"reflex": false,
"radius": 16
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"id": "11",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=55°、∠B=60°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"125°",
"5°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は55+60=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
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"y": 100.01979733405979,
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"showLabel": true
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"id": "C",
"x": 160,
"y": 215,
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"id": "D",
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"vertex": "B",
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"to": "C",
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"rightAngle": false,
"reflex": false,
"radius": 16
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],
"alt": "本文の点・辺・角に対応する図。"
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},
{
"id": "12",
"type": "choice",
"label": "三角形の外角",
"question": "△ABCで∠A=35°、∠B=80°です。BCをCの先へ延長した外角を選びなさい。",
"choices": [
"115°",
"65°",
"145°",
"45°"
],
"hint": "外角に隣り合わない二内角を使います。",
"explanation": "外角は35+80=115°です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "A",
"x": 66.44904710626976,
"y": 65.0,
"showLabel": true
},
{
"id": "B",
"x": 40,
"y": 215,
"showLabel": true
},
{
"id": "C",
"x": 136.39519582951954,
"y": 215,
"showLabel": true
},
{
"id": "D",
"x": 240,
"y": 252.85318053754162
}
],
"segments": [
{
"from": "C",
"to": "D"
}
],
"polygons": [
{
"points": [
"A",
"B",
"C"
] }
],
"labels": [],
"segmentMarks": [],
"angleMarks": [
{
"vertex": "A",
"from": "C",
"to": "B",
"label": "35°",
"rightAngle": false,
"reflex": false,
"radius": 16
},
{
"vertex": "B",
"from": "A",
"to": "C",
"label": "80°",
"rightAngle": false,
"reflex": false,
"radius": 16
}
],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "13",
"type": "choice",
"label": "平行の判定",
"question": "図で∠BOC=∠FPOと分かりました。AB∥EFといえる根拠を選びなさい。",
"choices": [
"同位角が等しいから",
"対頂角が等しいから",
"隣角の和が180°だから",
"図で同じ向きに見えるから"
],
"hint": "異なる交点の、同じ位置にある角です。",
"explanation": "同位角の等しさは二直線が平行になる条件です。",
"visual": {
"kind": "geometry",
"points": [
{
"id": "O",
"x": 120,
"y": 70,
"showLabel": true
},
{
"id": "A",
"x": 30,
"y": 70,
"showLabel": true
},
{
"id": "B",
"x": 245,
"y": 70,
"showLabel": true
},
{
"id": "C",
"x": 145.98076211353316,
"y": 25,
"showLabel": true
},
{
"id": "D",
"x": 68.03847577293367,
"y": 160,
"showLabel": true
},
{
"id": "P",
"x": 94.01923788646684,
"y": 115,
"showLabel": true
},
{
"id": "E",
"x": 30,
"y": 115,
"showLabel": true
},
{
"id": "F",
"x": 245,
"y": 115,
"showLabel": true
}
],
"segments": [
{
"from": "A",
"to": "B"
},
{
"from": "C",
"to": "D"
},
{
"from": "E",
"to": "F"
}
],
"polygons": [],
"labels": [],
"segmentMarks": [],
"angleMarks": [],
"alt": "本文の点・辺・角に対応する図。"
}
},
{
"id": "14",
"type": "choice",
"label": "性質と条件",
"question": "「二直線の錯角が等しければ二直線は平行」の仮定を選びなさい。",
"choices": [
"錯角が等しい",
"二直線が平行",
"対頂角が等しい",
"三角形の内角和が180°"
],
"hint": "「〜ならば」の前が与えられた条件です。",
"explanation": "錯角の等しさを仮定し、平行を結論にしています。"
},
{
"id": "15",
"type": "choice",
"label": "内角と外角",
"question": "三角形の内角が125°の頂点の、隣り合う外角を選びなさい。",
"choices": [
"55°",
"125°",
"235°",
"180°"
],
"hint": "内角と隣の外角で一直線になります。",
"explanation": "180−125=55°です。"
}
] }
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- デジタルドリル(数学)