Three triangles can be obtained by drawing one line segment in a triangle, and how many triangles can be obtained by drawing 10 line segments

Three triangles can be obtained by drawing one line segment in a triangle, and how many triangles can be obtained by drawing 10 line segments

Draw a line to get three triangles, that is 1 + 2 = 3
Draw two lines to get six triangles, namely 1 + 2 + 3 = 6
Draw three lines to get 10 triangles, that is 1 + 2 + 3 + 4 = 10
Launched in this category
Draw 10 lines to get 66 triangles, that is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 11 * 12 / 2 = 66

How to divide a Pentagon into two triangles with a line

If it's a concave Pentagon, it's easy

How to get two triangles by dividing Pentagon with a line

Because the lines drawn are common, one triangle has two sides, and the other triangle has two different sides. There are only four sides in total, so the proposition is impossible

How can a regular pentagon be divided into two triangles by a straight line
When is this a Mathematical Olympiad problem
You can't make any line outside the graph... Inside the graph

It's a Mathematical Olympiad,
Let the regular pentagon be ABCDE,
Make two parallel lines am ⊥ AB, BN ⊥ AB through ab,
Two parallel lines are a thick line to be made,
With a brush, the thick line width is ab line length
Theoretical basis:
In plane geometry, a straight line has no width,
A wide line is not a straight line

How can a Pentagon and a pen become two triangles, not thick lines
Please draw a picture,

It's possible. Generally we see convex polygons, but in fact this figure is concave Pentagon

Add a line and divide into two triangles

How many angles does a triangle have? If you add a line segment to the triangle, how many angles less than 180 degrees will be added? What about adding a line segment
How many angles does a triangle have? If you add a line segment to the triangle, how many less than 180 angles will be added
Degree angle? Drawing a line segment?

(1) Three corners
(2) Add 4
(3) 12 more

Starting from the angle of a triangle, how many triangles can be added for each additional line segment? What's the rule? How to express it?

If you only start from one corner, it must be one. If you start from different corners, it's hard to say

In the graph, there are three points on the parallel line L1 L2. How many triangles can be drawn if these points are vertices?
Let me give you a general picture
There are three points ABC on the parallel line L1
There are three points of def on the parallel line L2
There is a triangle in the middle (ABE)
What's the formula

There are three methods to select a point on L1, corresponding to each method of L1. There are three methods to select two points from three points on L2, so there can be nine triangles. Similarly, there can be nine triangles from any two of three points on L1, and then there can be nine triangles from any one of three points on L2

In the following blank space, draw a unique and meaningful figure and write one or two appropriate and humorous commentaries, such as