How to solve geometry problems? Many students have been asking this question over the years. Sometimes even the subject itself causes fear and disgust due to a lack of understanding of certain topics. Then it can be very difficult to overcome the dislike for geometry and again attend lessons with interest.
What is the reason for the problem of solving problems in geometry?
It largely depends on how the teacher explains his subject. If the teacher can get the students interested, then things will go on a knurled, and each lesson will be exciting. Children will even stay during recess in order to have time to solve as many problems as possible.
If this subject was explained poorly to you or if there are some other reasons why you are completely unable to delve into the topic, this article will help you figure it out.
How to learn to solve problems in geometry?
First you need to understand that in one day you are unlikely to advance far in your knowledge, so tune in to a long learning process.
You also need to decide on the goal. If you just need to solve a geometry problem in order not to get a bad grade on the test, you just need to learn a certain topic and practice some practical aspects.
What to do?
Grab your textbook and flip through the last few paragraphs you’ve learned. Try to delve into the information, understand that how your knowledge will be assessed depends on it. Now you can take a piece of paper and study several problems, be sure to look at the text of the textbook and try to understand the solution algorithm.
If something does not work out, refer to the Solution book, which was released specifically for your textbook. Just do not write off absolutely everything, try to understand how to solve geometry problems.
Remember what the teacher said in the classroom, perhaps some information will be useful.
The human factor should not be neglected either. Schoolchildren or students who know the subject well will not refuse to help you. Some of them can explain much more clearly than teachers.
And for those who decided not just to understand individual topics, but to learn how to solve problems and how to crack nuts, you need to work hard.
First, the main thing is to motivate yourself for further activities. It so happens that the question of how to learn how to solve problems in geometry arises only once, and then it just starts copying examples from the Internet. It is highly undesirable to do so.
Develop perseverance. It is much easier to look at the Solution book, of course, but think about how much pleasure you will experience when you solve a difficult problem on your own. Therefore, it is better to sit for an extra half hour at a textbook than to try to quickly write off someone’s decision.
Maybe you will need geometry for your future profession. Then, all the more, you should not postpone the matter indefinitely, you need to take on tasks right now.
Secondly, practice, and only practice, will help you get one step closer to your goal!
Get in the habit of learning new things every day. Just try to solve one problem in the morning, and then check its correctness using the keys. Later, you will notice that every day the process is going faster and better.
The most important thing here is not to give up and not pay attention to minor difficulties. If you include this advice in your daily routine, then the question of how to solve geometry problems will disappear by itself.
At school, do not be afraid to raise your hand once again and go to the blackboard to solve a difficult example that no one dared to comprehend. Even if something goes wrong and you fail to complete the task, there is nothing wrong with that. The instructor will explain the solution to the example and even praise you for your courage. It is also a good way to show your knowledge to classmates.
Guys can help with assignments when they find out that you are serious about your subject.
How to solve geometry problems
Geometry often causes problems because it is not clear which side to take on the task. And it seems you know all the theorems, but you don’t know which one should be applied. Therefore, we have compiled a small cheat sheet-algorithm for solving problems. The actions described in it do not have to do everything, you do exactly as much as is necessary to find a solution. And you look at each next item of the cheat sheet only if the previous one did not work.
So, when you have read the problem and made a drawing and do not understand how to find the answer, you:
1. Determine the main figure of the problem (trapezoid, triangle, parallelogram).
2. Find out whether it is “wonderful”, that is, a special case of some figure
3. You look at the question. If you need to find an angle or a side, then designate them with X. If you need to find an area or perimeter or something else that is calculated by a formula, write a formula and mark on the drawing the elements you need to calculate.
4. You remember all the theorems and properties associated with your figure. There is no need to rush to sort them out in order, but if you think about them at least for a second, maybe the necessary theorem will pop up in your memory. Keep in mind what you need to find at all times.
5. Once again you read the condition, slowly and in detail. You stop at every place where new information is given, and remember all the theorems and properties associated with this new information
6. Find all corners and sides
7. You try to find similar triangles and if you find them, then you apply their properties
8. You try to find equal triangles and if you find them, you apply their properties
Do not forget that you can apply not only theorems to your particular case of a figure, but also more general ones. If you have a right-angled triangle, remember that it is still a triangle and all general theorems and properties of triangles apply to it, as to any other triangle.
Examples of problem solving
Objective 1.
In triangle ABC, point D on side AB is chosen so that AC = AD. Angle A of triangle ABC is 16 ° and angle ACB is 134 °. Find the DCB angle.
Solution: From triangle ADC you can see that it is isosceles because its 2 sides are equal.
And in an isosceles triangle, the angles at the base are equal.
Hence, the ADC angle is equal to the ACB angle.
But the sum of the interior angles of the triangle is 180 °.
Hence, the sum of the two angles at the base is 180-16 = 164 °.
The angles, as we said, are equal. Therefore, each of them is equal to 164: 2 = 82 °.
The ACB angle is equal to 134 ° by condition.
And if you draw a ray inside the corner, then it will divide the angle into 2 angles, the sum of the degree measures of which will be equal to the degree measure of the original angle.
Those. Angle ACB is equal to the sum of angles АCD and DCB.
Hence, the DCB angle is 134 – 82 = 52 °.
Answer: The DCB angle is 52 °.
Objective 2.
Two segments AC and BD intersect at point O. Moreover, AO = CO and ∠A = ∠C. Prove that triangles AOB and OC are equal.
Proof: The desired triangles have one equal side and one equal angle. So, according to the signs of equality of triangles, we also need either one equal side, or one equal angle.
The sides are somehow not visible, but you can still find it at an equal angle.
The corners AOB and DOC are vertical.
And the vertical angles, as we know, are equal.
In each of the triangles we have an equal side and two equal angles adjacent to it.
Triangles are equal in 2 signs.
Objective 3.
The bisector AK is drawn in the triangle ABC. The AKS angle is 94 ° and the ABC angle is 62 °. Find the angle C of triangle ABC.
Solution: Angle AKS is external for triangle ABK and is equal to the sum of two internal angles that are not adjacent to it, i.e. the sum of the angles B and VAK.
From here we can find the VAK angle.
It is equal to 94 – 62 = 32 °.
Since AK is the bisector of angle A, the angle KAS is also 32 °.
And now, looking at the AKC triangle and knowing 2 angles in it, you can find the third one.
∠С = 180 – 32 – 94 = 54 °.
Answer: angle C is 54 °.
Objective 4.
In the triangle ABC, the sides of the AC and AB are equal to each other. The outside angle at the apex B is 110 °. Find the angle C.
Solution: The outer angle B is 110 °, which means that the adjacent inner angle in the triangle is
180-10 = 70 °.
But the inner angle B is equal to the angle A, as are the angles at the base of an isosceles triangle. Hence, the angle A is equal to 70 °.
And the sum of the interior angles of the triangle is 180 °.
And if 2 of them are equal to 70, then the third angle C accounts for 180 – 70 – 70 = 40 °.
Answer: the angle c is 40 °.
Objective 5.
In the triangle ABC heights are drawn, which intersect at point O. The angle of the COW is 119 °. Find the angle A.
Solution: The PTO angle is adjacent to the COM angle and is equal to 180-119 = 61 °.
The angle SMA is external in the triangle CMB and is equal to the sum of two internal, not adjacent to it.
Hence, the OBM angle is 90-61 = 29 °.
And from the right-angled triangle ВКА you can find the angle А, because the sum of the acute angles in a right-angled triangle is 90 °.
This means that the angle A is 90 – 29 = 61 °.
Answer: Angle A is 61 °.
What to do if you can’t solve the problem
Don’t be discouraged if no one responded to your request. You can always ask for help from a tutor who will explain exactly how to solve a geometry problem. Even with a limited amount of money, Skype classes will be a good way out, which are no worse than the lessons that take place in person.
That’s all the advice. Hopefully, you’ve figured out how to solve geometry problems. In any case, try to apply these methods in practice, and you will implement your plan!
