Putting a triangle with seven matches can pose two situations: the three sides are 1, 3, 3 or 2, 2, 3.
Hands-on experiments, it is easy to verify the above facts, and there is really no more situation.
(1) Please guess, how many different situations can you put a triangle with eight matches?
(2) Hands-on experiments to see if we can put forward several different situations.
(3) Use what you have learned to answer what different situations can be put on a triangle with ten matches, and draw a schematic diagram.
To analyze this example, we only need to do sub-topic (3).
The knowledge to be used is the relationship between three sides of a triangle, that is, the sum of any two sides in a triangle is greater than the third side.
There are many matches. When considering how to allocate 65,438+00 matches, it is easy to be duplicated or omitted. For example, after analyzing the situation that the lengths of three sides are 2, 3 and 5 respectively, it is analyzed that the lengths of three sides are 3, 5 and 2 respectively, which forms unnecessary repetition.
Therefore, we can first assume the number of matches used on the shortest side and finally determine the number of matches used on the longest side.
So we can know that the matching of 10 is divided into three groups, and there are the following possibilities:
1, 1,8; 1,2,7; 1,3,6; 1,4,5; 2,2,6; 2,3,5; 2,4,4; 3,3,4.
Just analyze the above eight situations and see if each situation can form a triangle.
It depends on whether the sum of two shorter line segments is greater than the third line segment. The "line segment" here is made up of matches.
Making tables can make the analysis results more obvious and help to avoid mistakes.
(the shortest)
(shorter)
(longest)
The relationship between size and
Can you form a triangle?
1
1 8
×
1
2
seven
×
1
three
six
×
1
four
five
×
2
2
six
×
2
three
five
×
2
four
four
√
three
three
four
√
Solving (1) conjecture can put forward at least two different situations;
(2) Only two different situations can be put forward. The number of matches used on three sides is 2, 3 and 3 respectively.
(3) Two different situations can be put forward. The number of matches used on three sides is 2, 4, 4 or 3, 3 and 4 respectively.
Facts show that the guess of the problem (1) here is incorrect. This phenomenon is as normal as guessing the correct result of many questions. However, just because speculation may be wrong, it cannot be said that speculation is not important, nor can it make people unwilling to guess. Without speculation, many truths will not be recognized by human beings.
This problem is also an example of using the idea of classification.
For this topic, it is difficult to gain much by just looking at it, and you need to do it yourself.
Judging whether three line segments can form a triangle, as long as the sum of two shorter line segments is greater than the longest line segment, this can be understood through experiments (take several groups of three fixed-length line segments to see if a triangle can be formed).