角度の性質と多边形の推論 · ハイレベル
導入済み| English | 意味 |
|---|---|
| corresponding angles/ˌkɒrɪˈspɒndɪŋ ˈæŋɡlz/ | 対応角 |
A surveyor measures one angle where a road crosses two parallel boundaries. Parallelism allows another angle to be deduced without measuring it.
- A surveyor measures one angle where a road crosses two parallel boundaries. Parallelism allows another angle to be deduced without measuring it.
- This lesson studies corresponding angles 同位角: Angles in matching positions at a transversal crossing two lines.
Choose the mathematical structure
- Angles around one point sum to 360°; angles on a straight line sum to 180°; vertically opposite angles are equal. When the crossed lines are parallel, corresponding and alternate angles are equal and co-interior angles sum to 180°. A triangle has angle sum 180°. Split an n-sided polygon into n-2 triangles to derive its interior sum (n-2)×180°.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
同位角が等しくなるのはいつか？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
同位角、内側交角、外側交角の法則は平行線の「性質」である。平行でなければ等しさは成り立たないため、証明では理由を明記する必要がある。
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
If a straight-line angle is 68°, its neighbour is 112°; its vertically opposite angle is 68°. A parallel-line corresponding angle is also 68°, with the reason named. Drawing a line through a triangle vertex parallel to the opposite side transfers its two base angles by alternate-angle equality; the three angles then form a straight line and sum to 180°. A pentagon splits into three triangles, giving 540°. A regular hexagon has total 720°, each interior angle 120° and each exterior turn 60°. Exterior turns of a convex polygon sum to one full turn, 360°; a regular polygon with turn 45° has eight sides.
角度の性質と多边形の推論
一点を取り囲む角の和は 360°；一直線上の角の和は 180°；対頂角は等しい
例題の命題を分類し、それぞれの判断を正当化する単位または不変量を説明せよ。
68°の補角（直線上の隣り合う角）を求めよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
180-68=112°.
Test a tempting shortcut
- Corresponding/alternate equalities require parallel lines. Name the theorem rather than using informal letter-shape labels. An interior angle is not the same as an exterior turning angle.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
Corresponding angles are equal even when the crossed lines are not parallel. This claim is false. Explain which definition or assumption it violates.
五角形の内角の和を求めよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
(5-2)×180=540°.
対応角は、交わる線が平行であっても等しい。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
対応角・内錯角の相等には平行線が必要である。定理の名前を述べるべきであり、非公式な文字形状ラベルを用いてはならない。内角と外側の転回角は異なる概念である。
Interpret a new situation
- AQA G3/G6 expects reasons and derivations. Mark the given parallelism, identify the angle positions and build a chain of justified equalities rather than reading angles from a sketch.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
正六角形の外角の一つを求めよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
360/6=60°.
各角度に関する法則と値または規則を対応させよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
n角形をn-2個の三角形に分割することで、三角形の内角和の法則180°から内角の総和を導く。
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
Angles in matching positions at a transversal crossing two lines. Choose the relationship, show the method, check its assumptions and interpret the result.