7日間コース
Master Triangles & Quadrilaterals in 7 Days
Master isosceles triangles, right triangle congruence, parallelogram properties, and special quadrilateral conditions through understanding and proof.
対象: Junior High 2 / Overseas Japanese students
Concepts & Worked Examples
Isosceles/right triangle properties, parallelogram conditions, and special quadrilaterals.
定義： 2つの辺が等しい三角形。等しい辺を等辺、残りを底辺という。
例：頂角40°の二等辺三角形 → 底角 = (180° − 40°)/2 = 70° 例：底角72°の二等辺三角形 → 頂角 = 180° − 144° = 36°
2つの角が等しい → その三角形は二等辺三角形（逆）。
通常の合同条件に加え、直角三角形には特別な条件がある：
斜辺と1辺（HL）： 斜辺と他の1辺がそれぞれ等しい → 合同
定義： 2組の対辺がそれぞれ平行な四角形。
以下のどれか1つが成り立てば平行四辺形：
→ 対角線の長さが等しい
→ 対角線が垂直に交わる
→ 両方の性質を持つ
An isosceles triangle has a base angle of 65°. Find the vertex angle.
解答
180° − 65° × 2 = 180° − 130° = 50°
Sum of angles = 180°. Two base angles are equal.
Name 3 properties of a parallelogram.
解答
1. Opposite sides are equal 2. Opposite angles are equal 3. Diagonals bisect each other
These are the fundamental properties that follow from the definition.
Which special parallelogram has perpendicular diagonals?
解答
Rhombus (ひし形)
A rhombus has all sides equal, and its diagonals cross at right angles.
Basic Practice
Isosceles angles, parallelogram properties, and identifying special quads.
三角形と四角形の性質を練習。
Isosceles triangle, vertex angle = 100°. Find base angles.
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答え
40° each
In parallelogram ABCD, ∠A = 70°. Find ∠B.
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答え
110° (adjacent angles are supplementary)
Parallelogram diagonals are equal. What special type is it?
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答え
Rectangle (長方形)
ABCD is a parallelogram. AB = 8, BC = 5. Find CD and DA.
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答え
CD = 8, DA = 5
Name the extra congruence condition for right triangles.
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答え
HL (Hypotenuse-Leg): hypotenuse and one leg equal
Standard Practice
Proofs with isosceles triangles and parallelograms. ★2-3.
Pattern Practice
All triangle/quadrilateral proof patterns. ★2-3.
Applied Practice
Multi-step proofs and condition checking. ★3-4.
Advanced Practice
Complex proofs combining multiple theorems. ★4-5.
Final Test & Bridge to Next
Comprehensive test. Preview of similarity.