How to solve geometry problems in junior high school mathematics

How to solve geometry problems in junior high school mathematics

If there is no idea, list out the known conditions, then write down the conclusions directly obtained from the known conditions, and then write down the conclusions that can be obtained step by step

Junior high school mathematics geometry problem-solving method in addition to "cut short" what other problem-solving methods?
It's better to state the specific application

Truncation is a way to prove that one line segment is equal to the sum or difference of the other two lines
The auxiliary line methods of geometry problems include the middle line method and the extended middle line method
Having an isosceles triangle as the base
The circle angle of diameter connection is 90 degrees
Congruence of constructed triangles
Translation or rotation

It is proved that if a makes a square matrix of order n and a is not equal to o, then there exists a nonzero matrix B such that ab = o if and only if the determinant of a is 0

Proof: necessity
Because there is a nonzero matrix B such that ab = o
So the column vectors of B are the solution vectors of AX = 0
So AX = 0 has a nonzero solution
So | a | = 0
adequacy.
Because | a | = 0, ax = 0 has nonzero solutions B1,..., BS
Let B = (B1,..., BS)
Then AB = 0

In English grammar "plural form of noun", there are "special nouns which can have two plural nouns"
Please see note format!
For example: Zero -- zeros -- zeroes -- zero

Starf ~ starfs ~ starves ~ scarves

1. When a batch of books are delivered to the bookstore, 5 / 12 of the total books are sold on the first day, 30 of the remaining 1 / 4 are sold on the second day, and 180 are left. How many books are there in this batch?
2. The innovative oil factory has transported 280 tons of rapeseed, and the oil yield is 38%. Now 95 tons of rapeseed have been squeezed out. What percentage of this batch of rapeseed will be used?
3. A canal has been built for 1.5km, and the rest is 2 / 5 more than the one already built. What is the remaining part of the total length?
4. There are 1020 parts in a batch. Party A makes 80 parts per hour, Party B makes 60 parts per hour, Party C makes 70 parts per hour, Party A and Party C cooperate for 4 hours, and Party B joins in to make them together. How many hours will it take to complete them?
5. A steel plant produces 420 tons of steel in one day, 1 / 2 tons more in the second day than in the first day, and 1 / 5 less in the third day than in the previous two days. How many tons in three days?
6. For a batch of parts, two fifths of them were made on the first day, and half of them were made on the other two days. It is known that seven more parts were made on the first day than on the next two days. How many parts are there?
7. The number of primary school students who reached the standard in the first semester was 11 / 22. In this semester, another 120 students reached the standard, and the standard rate of the whole school rose to 3 / 4. How many students did not reach the standard?

The first question: "there are 30 copies of the remaining 1 / 4 sold the next day". This condition is wrong. It should be "sell the remaining 1 / 4 and 30 copies the next day" (180 + 30) / [1 - (5 / 12 + 7 / 48)] = 4802, (280-95 / 38%) / 280 = 0.893 = 89.3% 3, (1 + 2 / 5) / (1 + 1 + 2 / 5) = 7 / 124, 4 + [1020-4x (80 + 70)] / (80 +... "

A square has an area of 40 square centimeters. Draw the largest triangle in it. The area of the triangle is（

A square has an area of 40 square centimeters. Draw the largest triangle in it. The area of the triangle is (20 square centimeters)

English translation
What I want to express is
This is my most precious memory
Thank you for your reply on the first floor.
This is the most beautiful memory in my heart
(thank you for your reply on the third floor) hee hee, I think so too!

this is the most precious memory in my mind

A cuboid is 30 cm long and 20 cm wide. It contains water 10 cm deep. Now there is a cuboid iron block 8 cm long and 8 cm wide and 15 cm high（
The meaning should also be changed
(1) Put the iron into the water horizontally, and the water will rise for several meters
(2) Put the iron block upright into the water and the water will rise for several meters

(8 * 8 * 15) / (30 * 20) = 1.6cm
Level up 1.6 cm, now the water is 11.6 cm high
I can only answer so many questions because I can't see your questions,

In the cube abcd-a1b1c1d1 with edge length 2, e and F are the moving points on edge AB and BC respectively, and AE = BF
1. Verification: a1f is perpendicular to C1E
2. When E and F are the midpoint of AB and BC respectively, the dihedral angle b1-ef-b is calculated
Why is a1f perpendicular to de, C1d?

Connect De, C1d
A1f perpendicular to de, C1d
So a1f is perpendicular to C1E
Make ef through B and intersect EF with H
Angle b1bh is the plane angle
2 times the root of arctan
C1d is perpendicular to plane a1d1cf
De vertical plane aa1f

how to make cake
must be in a sipple way

hi
let me to share with you the way of making a cake,which is the simple way.
Making cake in microwave oven
Ingredients: 100 grams of dried flour, 5 grams of granulated sugar, 30 grams of butter, 45 grams of milk, 1 tablespoons of cream, and a few drops of cream.
1: first, mix eggs and sugar with egg whisk to make bubbles.
2: put the flour, baking powder, butter (melted in advance with microwave heating), milk and cream flavors together into the egg, stirring evenly.
3: Pour the batter into the surface of the container
Smooth, then cover it with plastic wrap and put it in the microwave oven. During heating, prick it with bamboo stick from time to time
Until there is no more liquid on the bamboo stick, it means that it has been baked successfully
4: Take out the baked cake and decorate it with cream and fruit as you like
Maybe it's not as loose as the oven, but it's soft and delicious, but it's convenient
With fresh cream and fruit decoration should be OK! The most important thing is the heart
tks