Unit 7
Paksi Simetri
Hana membuat sebuah wau kertas.
Dia melipat wau itu tepat di tengah. Kedua-dua bahagian bertindih tepat.
Garis lipatan itu dipanggil paksi simetri.
对称轴 = paksi simetri
Hana 做了一个纸风筝（wau）。她把风筝从正中间对折，左右两半刚好完全叠在一起，一点也没有多出来。这条折痕就叫对称轴。这一课学怎样判断一条线是不是对称轴，还要数图形有几条对称轴。
例子：把一张爱心形的纸从中间对折，两边会完全重合。
注意：对折后“完全重合”才算，差一点点都不行。
line of symmetry = paksi simetri
Hana makes a paper kite (wau). She folds it exactly down the middle, and the two halves lie perfectly on top of each other with nothing sticking out. That fold line is called a line of symmetry. In this unit we learn to test whether a line is a line of symmetry and to count how many lines a shape has.
Example: a paper heart folded down its middle has two halves that match exactly.
Watch out: the halves must match exactly; nearly matching is not enough.
Lihat
Lipat dan semak
Bertindih tepat? → paksi simetri
dua bahagian sama saiz dan sama bentuk
对折检查 = lipat dan semak
动画里房子的右半边沿着中间的线翻过来，盖在左半边上，形状和大小完全一样，叫“bertindih tepat”（完全重合）。再打开，那条折线就是对称轴。对称轴把图形分成两半，两半一样大、一样形状，像照镜子一样。
例子：蝴蝶的身体就像一条对称轴，左右翅膀一样。
注意：两半要一样大还要一样形状，只是一样大不够。
fold and check = lipat dan semak
In the animation, the right half of the house flips over along the middle line and covers the left half exactly, same shape and same size; this is called bertindih tepat. When it opens again, the fold line is the line of symmetry. It splits the shape into two halves that match like a mirror image.
Example: a butterfly's body acts like a line of symmetry, with matching wings on each side.
Watch out: the halves must match in shape as well as size; equal size alone is not enough.
Cuba
Adakah garis putus-putus ini paksi simetri?
判断对称轴 = tentukan paksi simetri
这个三角形两条斜边一样长，虚线从尖顶直直往下，穿过底边的正中间。沿着它对折，左半边和右半边会完全重合，所以这条虚线是对称轴。对称轴不一定是横的，竖的、斜的都可以。
例子：等腰三角形的屋顶，从屋顶尖往下的直线就是对称轴。
注意：判断时想象真的把纸折起来，看两边能不能刚好盖住。
deciding on a line of symmetry = tentukan paksi simetri
This triangle has two equal slanted sides, and the dashed line runs straight down from the top point through the middle of the base. Folding along it makes the left half cover the right half exactly, so the dashed line is a line of symmetry. A line of symmetry can be upright, flat or slanting.
Example: on a triangle-shaped roof, the line straight down from the peak is a line of symmetry.
Watch out: imagine really folding the paper and check whether the halves cover each other exactly.
Awas!
Pepenjuru segi empat tepat
Lipat pada garis serong → tidak bertindih tepat
bahagian oren terkeluar → bukan paksi simetri
长方形的对角线 = pepenjuru segi empat tepat
很多同学以为长方形从一个角到对面角的斜线是对称轴。真的折一折：折过去的三角形（橙色）会跑到长方形外面，有一部分露出来，和下面的三角形不重合。所以长方形的对角线不是对称轴。长方形只有横、竖两条对称轴。
例子：拿一张 A4 纸沿对角线折，纸角会多出来。
注意：正方形的对角线才是对称轴，长方形不是。
diagonal of a rectangle = pepenjuru segi empat tepat
Many pupils think the slanting line from one corner of a rectangle to the opposite corner is a line of symmetry. Try folding: the folded triangle (orange) sticks out beyond the rectangle and does not match the triangle underneath. So a rectangle's diagonal is not a line of symmetry; a rectangle has only its upright and flat lines.
Example: fold an A4 sheet along its diagonal and the corners poke out.
Watch out: a square's diagonal is a line of symmetry, but a rectangle's is not.
Makmal lipat simetri
Pilih satu bentuk dan satu garis. Bertindih tepat atau tidak?
实验台：对折 = makmal lipat simetri；竖 = menegak；横 = mengufuk；斜 = serong
先选一个图形（长方形、正方形或房子），再选一条线：竖线、横线或斜线。半个图形会沿着线翻过去。完全重合，这条线就是对称轴；有一部分跑出去，就不是。试满 3 种。
例子：长方形选竖线，两边完全重合。
注意：特别试一试长方形的斜线和正方形的斜线，结果不一样。
lab: folding = makmal lipat simetri; upright = menegak; flat = mengufuk; slanting = serong
Choose a shape (rectangle, square or house), then choose a line: upright, flat or slanting. Half the shape flips over along the line. If the halves match exactly, the line is a line of symmetry; if a part sticks out, it is not. Try 3 different cases.
Example: a rectangle folded on the upright line matches exactly.
Watch out: be sure to try the slanting line on both the rectangle and the square; the results differ.
Apa yang kamu lihat?
Segi empat sama dilipat pada garis serong. Apa yang berlaku?
正方形的斜线 = garis serong segi empat sama
正方形四条边一样长，沿着对角线折，折过去的三角形刚好盖住另一半，完全重合，所以正方形的斜线是对称轴。这和长方形不一样：长方形的斜线折过去会露出来。完全重合就一定是对称轴。
例子：方形的手帕对角折，会变成一个整齐的三角形。
注意：同样是斜线，图形不同，答案也不同。
slanting line on a square = garis serong segi empat sama
A square has four equal sides, so folding along its diagonal makes one triangle sit exactly on the other, a perfect match, which means the square's diagonal is a line of symmetry. This is different from a rectangle, whose diagonal fold sticks out. An exact match always means a line of symmetry.
Example: folding a square handkerchief corner to corner makes a neat triangle.
Watch out: the same kind of slanting line can give different answers on different shapes.
Poligon sekata
Berapa paksi simetri?
Poligon sekata: bilangan paksi = bilangan sisi
segi empat sama
4 paksi
4 paksi
pentagon
5 paksi
5 paksi
heksagon
6 paksi
6 paksi
ada paksi dari bucu ke bucu, dan dari tengah sisi ke tengah sisi
正多边形的对称轴 = paksi simetri poligon sekata
正多边形的对称轴条数等于它的边数：正方形 4 条，正五边形 5 条，正六边形 6 条。有的对称轴从一个顶点穿到对面；有的从一条边的中点穿到对面边的中点。两种都要数，才不会漏。
例子：正八边形有 8 条边，所以有 8 条对称轴。
注意：正六边形只数“顶点到顶点”的话只有 3 条，会漏掉另外 3 条。
lines of symmetry of regular polygons = paksi simetri poligon sekata
A regular polygon has as many lines of symmetry as sides: a square has 4, a regular pentagon 5, a regular hexagon 6. Some lines go from a corner across to the opposite side; others join the middles of opposite sides. Count both kinds so none is missed.
Example: a regular octagon has 8 sides, so it has 8 lines of symmetry.
Watch out: counting only corner-to-corner lines on a hexagon gives 3 and misses the other 3.
Cuba
Berapakah bilangan paksi simetri sebuah oktagon sekata?
八边形的对称轴 = paksi simetri oktagon
正八边形有 8 条边。正多边形的对称轴数等于边数，所以有 8 条：4 条从顶点到对面顶点，4 条从边的中点到对面边的中点。选 4 是只数了其中一种。
例子：正五边形 5 条边 → 5 条对称轴。
注意：只有“正”多边形才有这个规律，长方形 4 条边却只有 2 条对称轴。
lines of symmetry of an octagon = paksi simetri oktagon
A regular octagon has 8 sides, and a regular polygon has as many lines of symmetry as sides, so it has 8: 4 joining opposite corners and 4 joining the middles of opposite sides. Choosing 4 counts only one kind.
Example: a regular pentagon has 5 sides and so 5 lines of symmetry.
Watch out: the rule works only for regular polygons; a rectangle has 4 sides but only 2 lines.
Bukan semua bentuk
Bentuk tanpa paksi simetri
Lipat ke mana-mana pun, tidak bertindih tepat
segi empat selari
0 paksi
0 paksi
bentuk L
0 paksi
0 paksi
segi empat tepat
2 paksi
2 paksi
没有对称轴的图形 = bentuk tanpa paksi simetri
不是每个图形都有对称轴。平行四边形不管竖折、横折还是斜折，总有一个角跑出去，所以它没有对称轴。L 形也一样。对比一下：长方形有横、竖 2 条对称轴。
例子：英文字母 F 也找不到对称轴。
注意：平行四边形看起来很整齐，但没有对称轴，很多同学会答错。
shapes with no line of symmetry = bentuk tanpa paksi simetri
Not every shape has a line of symmetry. However you fold a parallelogram, upright, flat or slanting, one corner always sticks out, so it has none. The L shape has none either. Compare the rectangle, which has 2 lines, one upright and one flat.
Example: the capital letter F has no line of symmetry either.
Watch out: a parallelogram looks neat, yet it has no line of symmetry, which trips up many pupils.
Padankan
Bentuk dan bilangan paksi
配对对称轴数 = padankan bilangan paksi
正方形：横、竖、两条斜线，一共 4 条。长方形：只有横、竖 2 条，斜线不算。房子：只有中间竖的 1 条。平行四边形：一条也没有，是 0。每个图形都试着竖折、横折、斜折，再数能完全重合的线。
例子：等腰三角形只有 1 条对称轴。
注意：长方形最容易多数成 4 条。
matching the number of lines = padankan bilangan paksi
Square: upright, flat and both diagonals, 4 lines. Rectangle: only upright and flat, 2 lines, since its diagonals do not count. House: just the 1 upright line down the middle. Parallelogram: none at all, 0. Try upright, flat and slanting folds on each shape and count the lines that match exactly.
Example: an isosceles triangle has only 1 line of symmetry.
Watch out: the rectangle is the one most often over-counted as 4.
Ringkasan
Syabas!
lipat → bertindih tepat → paksi simetri
Paksi simetri membahagi bentuk kepada dua bahagian yang sama saiz dan sama bentuk. Pepenjuru segi empat tepat bukan paksi simetri. Poligon sekata: bilangan paksi = bilangan sisi.
Latihan tambahan →