🔲 四边形家族：平行与直角的排列组合🔲 The Quadrilateral Family: Parallels & Right Angles
上一片里，三角形的三个角拼成一条直线，等于 180°。这一片轮到四边形：🧮 小算盘机器人要给小店铺地砖。它发现：四个角拼起来正好是完整一圈 360°，而且四边形之间还藏着一条“升级链”。Last leaf, a triangle's three angles folded into one straight line — 180°. This leaf is about quadrilaterals: the little calculator robot is tiling its shop floor, and finds that four angles add up to a full 360° turn — plus a hidden “level-up chain” between the family members.
第 1 步：四兄弟其实是一家人Step 1: Four shapes, one family
先认识四边形家族的四兄弟——它们不是并排站，而是层层升级出来的。Meet the family's four brothers — not standing side by side, but levelled up one condition at a time.
最底下是任意四边形；加上“两组对边分别平行”，升级成平行四边形；再各加一个条件，就长成矩形（加直角）或菱形（加四条边等长）。两个条件都加满，就是正方形——家族里“全都要”的顶配。At the base sits any quadrilateral; add “two pairs of parallel sides” and it levels up to a parallelogram. One more condition branches it into a rectangle (add right angles) or a rhombus (add four equal sides). Add both and you get the square — the family's all-in champion.
你可能会想：把平行四边形推歪、拉扁，四个角的大小都变了，总和还是 360° 吗？You might ask: push a parallelogram crooked and every angle changes — does the total stay 360°?
第 2 步：推一推，内角和不变Step 2: Push it — the angle sum stays
把平行四边形像衣架一样推来推去：一个角变大，对角跟着变大，邻角就变小——但四个角的总和死死钉在 360°。秘密是：沿一条对角线剪开，任意四边形都能分成两个三角形，180° + 180° = 360°。Push a parallelogram around like a clothes hanger: one angle grows, its opposite twin grows too, the neighbours shrink — yet the sum stays nailed to 360°. The secret: cut any quadrilateral along a diagonal and you get two triangles — 180° + 180° = 360°.
那这条“升级链”在生活里哪里见得到？So where do these level-ups show up in real life?
第 3 步：瓷砖店里的家族成员Step 3: Family members on the tile floor
瓷砖店就是四边形家族的展台：正方形砖四个 90° 角围住一点，拼满一圈正好 360°，所以能无缝铺满地面；菱形花砖、六边形砖也一样，靠“角拼起来是一圈”才不漏缝。选砖，其实是在选四边形的条件组合。A tile shop is the family's showroom: four square-tile corners of 90° meet at one point — a full 360° turn — so the floor covers with no gaps. Rhombus and hexagon tiles work the same way: angles that add up to a full turn leave no cracks. Choosing tiles is choosing a combination of conditions.
🎮 你来当家族鉴定师（30 秒）🎮 Your turn: family examiner (30 seconds)
道理讲完了。先拨动 3 个条件开关，看四边形怎么一步步升级；再接 4 张鉴定卡，认出每个成员。Theory done. Flip the 3 condition switches to level a quadrilateral up; then take 4 cards and name each family member.
一句话记住它：四边形家族是一棵树——两组对边平行让它成为平行四边形；再加直角是矩形，再加等长是菱形；两个都加是正方形。不管怎么推，内角和永远是 360°。Remember it in one line: the quadrilateral family is a tree — parallel sides make a parallelogram; add right angles for a rectangle, equal sides for a rhombus, and both for a square. Push it any way you like: the angles always add up to 360°.
平行四边形：两组对边分别平行；矩形和菱形都是它的“升级版”Parallelogram: two pairs of parallel sides — rectangle and rhombus are its upgraded versions矩形 = 平行四边形 + 四个直角；菱形 = 平行四边形 + 四条边等长Rectangle = parallelogram + four right angles; rhombus = parallelogram + four equal sides正方形两个条件全占；任意四边形内角和恒为 360°Square takes both conditions; any quadrilateral's angles always sum to 360°
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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