Hình 7A1 Tính góc Bài 7 #toan7

We will do problem number 7 Problem 7 Right triangle ABC Triangle ABC Right angle at A Altitude AH The bisector of angle BAH cuts BC at D The bisector of angle BAH This is the angle AD It is required to prove that angle ABH is equal to angle CAH ABH is called angle B It is equal to angle CAH It is called angle A Angles B and A are equal This is a familiar triangle It is obvious In a right triangle With the altitude AH When the triangle is placed on the altitude The acute angle will be equal to the angle Equal relationships between acute angles Obtuse angle Acute angle Angle B is equal to angle A This angle is equal to angle A The results are widely used in various areas of geometry With the bridge It was really very simple Because It is at angle For example This angle B this angle B is complementary to this angle A Why are they complementary Because we have triangle A B H which is a right triangle at point H right Right-angled at H Then the two acute angles are complementary Meanwhile we have this angle A and this angle A is two angles that are complementary Because the sum of them is equal to this larger angle A which is 90 degrees So we immediately have obviously this angle B and this angle A are equal Because they are both complementary to angle A right Both complementary to this angle A The proof is very simple But the point here is to help us remember Next time we will have a reflex when we encounter this configuration This angle A and angle C are equal too because they are both complementary to this angle A These two angles A are equal because they are both complementary to this angle A Even this angle A and angle C are equal why Does it complement angle B This angle A and this angle B are complementary Similarly this angle C and this angle B are also complementary right Therefore we also have this angle A and this angle C being equal Therefore proving that angle ABH is equal to angle CH is obvious Now let's move to the second point They asked me to prove the triangle Triangle CAD is CAD an isosceles triangle Then by observing the drawing I can deduce that it will balance at C Is that right From the drawing we have we can estimate that it will balance at C That means now to prove a triangle isosceles we have two common approaches First we prove that the angles are equal side AC is equal to side CD Second we prove the angles we prove that angle A is equal to angle D right Now we think about the angle of approac From the perspective of angles to prove that it is balanced at C we will prove that angle D is equal to angle A The angle DAC is complementary to angle A1 This is the angle A1 Here I will denote this angle as A1 This is angle 2 Does the DAC angle with angle A1 add up to the large angle A which is 90 degrees Therefore we have the supplementary angle DAC with angle A1 This A 90-degree angle Minus angle A1 Similarly now we have the D corner This angle D is added to this angle A2 equal to 90 degrees Why Why does D plus angle A2 equal 90 Because are these two acute angles of eight right angles You have to right Then the two acute angles of the eight right angles are complementary angles that add up to 90 degrees Therefore this D angle also corresponds with angle A2 We have the angle This angle is called angle CDA CDA At 90 degrees Subtract A2 But as you know angle A1 and A2 according to the assumption Is the bisector of angle BAH These BNC here mean that AD is the angle bisector And we have angle A1 equal to angle A2 Then A1 equals A2 This leads to the DAC and the CAD being equal In simple terms These two angles are equal because they are both complementary to two equal angles D is complementary to A2 This A is connected to A1 Since the two angles A1 and A2 are equal we can conclude that D and A are equal Actually the learning process is a subtle and gradual process of growth Why do we need to do simple exercises like this Why What's the point of making a test this easy Actually it's just to get used to the image Getting used to the image and having some reflexes Some results come in the next time When you encounter such a situation when you see a shape like this people call it a "shape " a street like this Then you don't need to think or guess anymore I don't have to think about it anymore We have an immediate reaction Actually if you want to fly high and far you first need to master and do the basics well Without the basics you can't go far