Drawing conic curve with Zenyang Geometer's Sketchpad

Drawing conic curve with Zenyang Geometer's Sketchpad

There are three methods
1. Treat it as equation graph;
2. Conic curve can be processed by two segment function image processing;
3. It can be drawn directly in polar coordinate system

How to make flip effect in Geometer's Sketchpad
For example, if you flip a triangle, how can you achieve dynamic effects when making axisymmetric graphics?

Select the triangle you want to make symmetry, double-click the axis of symmetry, and then select the reflection in the transformation. If you want to rotate or translate, you can do this

There are two ways to draw a line segment equal to a known line segment: one is to use a compass_____ Second, draw with a scale

Fix the tip of the compass on the end of the line segment, and then fix the other end of the compass on the other end of the line segment. The distance between the compasses is the distance of the line segment. Fix the tip of the compass on the end of the line segment you want, and draw an arc on the line with the other end. The intersection of the arc and the line is another point of the line segment

The line segment m is taken as an isosceles right triangle ABC so that its hypotenuse AB equals M
Only need practice, do not need map. Thank you!

First, make the vertical bisector of the line segment m, take the intersection point O, take o as the center and m as the diameter to make a circle. If it intersects with the vertical bisector of m at P and Q, then the two ends of M and P or Q form the required isosceles right triangle

Given the line segments a, B, C (a ＞ B ＞ C), draw a line segment equal to 3a-b - &

∵a>b＞c,
∴a-b>0,a-c/2>0,
3a-b-c/2>0,
There are line segments 3a-b - ½ C

As shown in the figure, given the line segments m and N, draw a line segment AB so that it is equal to 2m + n

As shown in the figure: Line AB = 2m + n

Given the line segment a, how to draw a line segment AB so that ab = a? (requirement: ruler drawing) mysterious array of Jiangsu Education Press

First draw a ray
Take a point as the center of the circle, a as the radius, do the circle intersection at AC and B to get the line AB and ab = a

How to make an angle equal to a known angle with a ruler and a compass?

Known: ∠ AOB,
Calculate: ∠ CDE so that: ∠ CDE = ∠ AOB,
Method:
1. Make any ray De,
2. Take the point o as the center of the circle and the appropriate length as the radius to make the arc intersection OA and ob at the points m and n,
3. Take point D as the center and the same length as the radius to make arc intersection de at point P,
4. Take point P as the center of the circle, take Mn as the radius, and make the arc at point C,
5. Pass through point C as ray DC
The CDE is the required value

Use a ruler and a compass to make a schematic diagram of an angle equal to a known angle, as follows, to show that the basis for ∠ a ′ o ′ B ′ = ∠ AOB is ()
A. （S.S.S.）B. （S.A.S.）C. （A.S.A.）D. （A.A.S.）

The steps of drawing are as follows: (1) draw an arc with o as the center and any length as the radius, intersecting OA and ob at points c and D respectively; (2) draw an arc with o 'as the center and OC length as the radius, intersecting o' a 'at point C'; (3) draw an arc with C 'as the center and CD length as the radius, intersecting o' B 'at point d'; (4) make a ray o 'B' passing through point d '. Therefore, a' o 'B' is the same as AOB In △ OCD and △ o ′ C ′ D ′, O ′ C ′ = OCO ′ D ′ = ODC ′ D ′ = CD, ≌ OCD ≌ o ′ C ′ D ′ (SSS), ≌ a ′ o ′ B ′ = AOB, it is obvious that the judgment method is SSS

What is the theoretical basis for making an angle equal to a known angle with a ruler and a compass?

The theoretical basis for making an angle equal to a known angle with a ruler and a compass is SSS