该图显示了一个形状为四边形 ABCD 的花园地图。地图的比例尺为 1 cm 代表 10 m。

(a)
使用圆规和直尺，作图：
1. ((i))
  AB 的垂直平分线，
2. ((ii))
  角 ABC 的角平分线。
(b)
雕像 S 位于花园 ABCD 内部，它距离 D 点 55 m，并且到 A 和 B 的距离相等。

标出 S 的准确位置。
(c)
松树 T 位于花园 ABCD 内部，它到 AB 和 BC 的距离相等，并且到 A 和 B 的距离相等。

标出 T 的准确位置。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

20(a)((i))

1. Construct equal-radius arcs from $A$ and $B$ and draw the bisector through their intersections.

Set the compass radius to more than half of $AB$ . With centre $A$ , draw arcs above and below $AB$ . Without changing the compass radius, with centre $B$ , draw arcs to intersect the first pair of arcs. Join the two arc intersection points with a straight line. This line is the perpendicular bisector of $AB$ .

答案

The perpendicular bisector of $AB$ is constructed: it crosses $AB$ at its midpoint and is perpendicular to $AB$ .

20(a)((ii))

1. Construct the angle bisector of $\angle ABC$ using equal-radius arcs.

With centre $B$ , draw an arc cutting $BA$ and $BC$ at two points. Using the same radius from these two points, draw arcs that intersect inside $\angle ABC$ . Join $B$ to this intersection point with a ruler. This line is the angle bisector of $\angle ABC$ .

答案

The angle bisector of $\angle ABC$ is constructed as a straight line from $B$ dividing $\angle ABC$ into two equal angles.

20(b)

1. Convert the actual distance from $D$ to a map distance.

Scale: $1\text{ cm}:10\text{ m}$ .

$55\text{ m}\div 10=5.5\text{ cm}$

So $S$ must be $5.5\text{ cm}$ from $D$ on the map.

2. Locate the point satisfying both conditions.

Since $S$ is equidistant from $A$ and $B$ , $S$ lies on the perpendicular bisector of $AB$ .

Using compasses, draw an arc or circle with centre $D$ and radius $5.5\text{ cm}$ .

The required point $S$ is the intersection of this circle with the perpendicular bisector of $AB$ that lies inside quadrilateral $ABCD$ .

答案

$S$ is the point inside $ABCD$ where the perpendicular bisector of $AB$ meets the circle with centre $D$ and radius $5.5\text{ cm}$ on the map.

20(c)

1. Identify and label the intersection satisfying both equidistance conditions.

Since $T$ is equidistant from $AB$ and $BC$ , it lies on the angle bisector of $\angle ABC$ .

Since $T$ is equidistant from $A$ and $B$ , it lies on the perpendicular bisector of $AB$ .

Therefore, label
$T=\text{ intersection of the angle bisector of }\angle ABC\text{ and the perpendicular bisector of }AB$
inside the quadrilateral $ABCD$ .

答案

$T$ is the point inside $ABCD$ where the angle bisector of $\angle ABC$ intersects the perpendicular bisector of $AB$ .

AI 分析，可能出错

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该图显示了一个形状为四边形 ABCD 的花园地图。 地图的比例尺为 1 cm 代表 10 m。