Hình 7A1: Bài 4- Hai tam giác bằng nhau #toan7

M is the midpoint of AB N is the midpoint of AC On the opposite ray of the NB pioneer Take point D so tha ND equals NB This means that N is the midpoint of BD On the opposite ray of MC take point E such that ME equals MC It is equivalent to M being the midpoint of EC Then From here we can see that M is the midpoint of AB and also the midpoint of CE Similarly N is the midpoint of BD And N is the midpoint of AC The problem states that Q is the midpoint of AD and P is the midpoint of BC Now we will prove the first part that AD is equal to AE As the initial problem statement shows the assumption is that many factors are equal so we can think in the direction of identifying equal triangles And there is one thing that is to prove that two line segments are equal we can prove it in many ways First prove that these two segments are corresponding sides of two equal triangles Second we can prove Due to the nature of the triangle these two sides are equal to the third side If two sides are equal to a third side they will be equal Of course we will have many other ideas Now let's observe the triangle that contains side AD We observe the triangle that contains side AD Then the cream will pay attention to this triangle which is the DNA Is that right And naturally the cream will also see that it will be equal to this triangle C BN Because a set of equal elements AN equals NC DN equals NB all according to the assumption And these two angles are vertical angles These two triangles are congruent by the side-angle-side case This leads to AD being equal to BC Because these are two The corresponding side of the two equal triangles Is that right We will summarize AD using BC Because This drawing We feel that AD and the This AE has the same role so Similarly we will check the event It is AE Then it will be the side of the triangle Sure I'll translate the given text according to the rules provided And this triangle is equal to the triangle MBC According to the side angle side case it is completely similar MA equals MB ME equals MC Then These two triangles are congruent by the side-angle- side case This leads to the conclusion that AE is equal We also have AE equal to BC okay So is that What did we summarize Kem summarized AD and BC equally Then I will also compress AE using BC again So according to the nature of the compression would AE and AD be compressed equally So we arrive at the solution for question 1 Now when it comes to equal straight segments Kem found out that her CD is equal to which side Which side is equal to the CD And which side will BE be on By looking at the diagram Kem can sense that her CD will be equal to AB right And her BE will be equal to AC But Kem How do you prove it That's something for Kem to think about The teacher won't say anything more Consider it a question Let Kem think some more That is the proof that CD equals AB And prove that BE equals AC please Now let's move on to sentence 2 To prove that A E D are collinear what should we do That is when we discovered the two NAD triangles NAD And the NCB sensory organ NCB These two triangles are equal Then Kem will get the angle NAD We will obtain this angle A And this angle C Is equal Is equal right But Consider these two straight lines And the third straight line cuts this way Then obviously angles A and C are in the correct alternate interior position right So then These two angles are in a cross position and are equal then we will get AD It will be parallel to BC Right Actually we ca Observe that AD and BC are parallel to each other through the diagram Then I go Prove that AD and BC are parallel by checking the equality of these two angles Then in the end it will lead to AD and BC being equal But if you look at the diagram first and then figure it out that's okay Observe that these two angles are equal Then I deduced that it can also be done in parallel That is whether I predict or prove it it's also acceptable Or you can prove it from your observation as well In conclusion I have that AD and BC are parallel to each other ThenSimilarly We will also prove that AD and BC are parallel to each other Because of this figure The AD part and the AEA part have a How is it They are symmetrical It has a They are similar to each other Now how do we prove that AD and BC are parallel So it is the same here Then we will prove this angle A By this angle B As shown above we also have two triangles EAM and CBM that are equal Therefore this angle A will be equal to this angle B because they are corresponding angles of two equal triangles So in conclusion we will get that AE and BC are parallel to each other There you know in Euclid 's axioms there is an axiom that says: Through a point outside a line There is only one straight line parallel to that line For example in this case of mine Through point A and line BC Then there is only one straight line parallel to BC But here we also have AD parallel to BC And AE is also parallel to BC So these AD and AE must be aligned because they are on the same straight line They must be aligned If lines AD and AE are overlapping it means that points A E and D are collinear and this is what we needed to prove That is it Then we have AD and AE AD and AE are parallel to BC Therefore we can conclude AD and AE are overlapping and three points A D E are collinear What needs to be proven We have completed proving question 2 However A very natural question for a math student is after finishing a problem then that is then there is a question is there another way This way of thinking is really good because it helps people become less stubborn and less rigid and it can broaden their minds It can expand the mind and help one not to be limited At the same time when understanding that there are many different paths to reach a truth This society is very vast the universe is even more vast And it is also very rich We should also cherish different people and different lives If we cultivate this way of thinking Good then I can think in many ways And math will help me with that thinking Training that way of thinking That's really great You all remember that There is another very common way to prove that three points are collinear That is by using the angle addition method What does that mean That is how we prove these three points Create a straight angle That is angle of 180 degrees In this figure we can label angle A1 Students can label angles A1 and A2 And A3 I can label the corners A1 A2 A3 like this The Are they equal The angle A1 is equal to the angle C Angle A2 is still angle A Is angle A3 equal to angle B The sum of angles A1 A2 A3 is equal to the sum of the three angles of a triangle ABC Is that correct Sum of 3 angles A1 A2 A3 It is the sum of the three angles in triangle ABC because A1 equals C A3 equals B and A2 is the angle A Because in a triangle Then the sum of the three angles is 180 degrees So we have immediately the three angles A1 A2 A3 are 180 degrees And therefore I concluded that angles D A and E are straight angles which measure 180 degrees Then we also get that A E D are collinear And thus we obtain the second solution Now let's hunt for the third structure To prove the The event is three points P L Q are collinear okay P L Q are collinear Then how will we proceed We can try the direction of the angle addition That is we will prove that angle P L Q is a straight angle I will prove that this angle is 180 degrees Remember the angle at A N Q is not vertical to the angle at C P It has not reached the peak why has it not reached the peak Because of the N N N P Q are not collinear you know My purpose is to prove that they are collinear So It is not aligned so it is not vertical Therefore we cannot use vertical if we do that is a misunderstanding In solving this geometry problem misconceptions often occur among new learners When you often have to press it multiple times then you will have fewer misunderstandings I need to go prove that it is straight Now let's take a closer look at the method of angle addition analysis like this The angle P N Q P N Q This is this corner Then it is P N C Equal to P N C Together with Q N C Angle P N Q equals angle P C plus angle C Q Now students observe this thing here Angle A N Q plus angle C Q also equals 180 degrees because it is equal to angle A C So now let's prove that angle P N C by angle A Q Our goal is to succeed right If we can now prove that angle A N Q equals angle C N P then at that time we can add the angle C N Q corner Then it will be 180 degrees right away So now okay It's the one The key to the solution is to prove to you that these two angles are equal But how do we prove that two angles are equal Usually we bring them down to two angles that is two angles Are the two triangles equal right Then Did the students notice The angle And the angle These angles L1 and L2 Are those two angles of the two triangles equal Of course the children will notice that triangle A N Q and triangle C N P Is that fair Firs First these are two equal angles Second A N equals C N Third A Q equals C P Why is A Q equal to C P Because A Q is half of A D right And C P is half of C P They are two equal sides because they are both half of two equal sides In conclusion the students will get a triangle A N Q are three collinear points And triangle C P are two congruent triangles By the side-angle-side case So we have the correct answer right Well here we will just write the answer If you want to present it simply you can present it yourself