There are two congruent triangles with two equal angles and one side. Why? Give a counterexample It is suggested to avoid the following multiple-choice questions when preparing the test paper Only the following elements of two triangles are equal, so it can't be determined that two triangles are congruent () (A) Two corners and one side; (b) two sides and included angle; (C) Three corners; (d) three sides We should strictly follow the format of "congruence of two triangles with two corners and the opposite side of one corner corresponding to the same". We should not omit "the opposite side of one corner". We should not use ambiguous language such as "congruence of two triangles with two corners and one side corresponding to the same" to determine congruence of two triangles in class In understanding this concept, do not confuse correspondence with the corresponding edge of congruent triangle. As long as two triangles have two equal angles and one equal side, we can regard these two triangles as having two equal angles and one equal side. It is emphasized in the textbook that there are two equal triangles corresponding to two corners and the opposite side of one corner. How to understand the correspondence here? First of all, I want to make it clear that correspondence and corresponding edge are not a concept. If we stand on the platform of congruence of triangles and understand the correspondence here based on the corresponding edge of congruence triangles, then this problem is very difficult to solve. I think the correspondence here has something in common with the correspondence in the concept of function. The first triangle has one side with a length of 3cm, and only the second triangle has one side with a length of 3cm. We should regard these two triangles as having a pair of equal sides, which means the correspondence here.

Not necessarily;
If the two corners are connected with this edge, they are congruent, otherwise they are not;
For example, if two similar right triangles, ∠ C = ∠ C ′ = 90 °, B = ∠ B ′ = 60 ° and ab = B ′ C ′, the two triangles are not congruent

It is proved that two angles and the opposite side of one of them correspond to two equal triangles congruent (intermittently "AAS")

Upstairs, junior high school did not learn what is reverse proposition ah ~ help him explain it!
prove:
Suppose that two angles and the opposite sides of one of them correspond to two equal triangles
Because two triangles have two equal angles,
So the two triangles are similar
Because these two similar triangles are not congruent,
So the opposite sides of the equal angles of the two triangles are not equal
This is in contradiction with the original proposition that the opposite sides of one corner are equal
So, the hypothesis doesn't hold
To sum up, the original proposition holds
The proof is complete

It is proved that two angles and the opposite side of one of them correspond to two identical triangles
Don't prove the law to the contrary
Hope to be able to map, with letters to prove, thank ~ ~ please!!

It's more difficult to map
It is known that: a = a ', ∠ B = B', AC = a'c '
Verification: △ ABC ≌ △ a'b'c '
∵∠A=∠A',∠B=∠B'
And ∠ a + B + C = ∠ a '+ B' + C '= 180 degree
∴∠C=∠C'
In △ ABC, △ a'b'c '
∠A=∠A'
AC=A'C'
∠C=∠C'
So: △ ABC ≌ a'b'c '(ASA)

The theorem of angles, sides and angles: two triangles whose angles and their clamped edges correspond to the same are congruent. It can be proved by me that the corresponding equality of two angles and any side can also be proved

That's right
Because the sum of the three angles is 180 degrees
So if two angles are equal, the third must be equal
In this way, it can be reduced to the corner theorem

If the median line length of an isosceles trapezoid is 6cm and the waist length is 5cm, then the circumference of the trapezoid is 5cm______ cm．

According to the median line theorem of trapezoid, the sum of the upper and lower base of trapezoid is 12. So the circumference is 12 + 10 = 22 (CM)

It is known that in △ ABC, the lengths of three sides a, B and C are all positive integers, and how many triangles satisfy the conditions that a is greater than or equal to B, B is greater than C, a = 5 and B = 7?

A = 5, B = 7. Why is a greater than or equal to b greater than C? How does a = B?

The willow beside the pond has six intervals. How many trees are there in all?
Mr. Li's house is on the sixth floor. How many floors does it take to climb from the first floor to the sixth floor?
South Lake fence has 9 iron chains, how many columns do you need?

Because the pond is round, 6-1 + 1 = 6 trees
Because the first floor does not need to climb, so a total of 6-1 = 5 floors
Because two pillars connect a chain, there are 9 + 1 = 10
Please adopt (> ^ ω)^

Primary school fifth grade mathematics problem: a square side length increases by 5 meters, the area increases by 95 square meters, how to find the area of the original square? How to solve with the formula?

If we know that the square side length increases by 5, the area increases by 95. Then we can set the original side length as a, then (a + 5) * (a + 5) - A * a = 95. Can you understand that? Then you can simplify the equation to 25 + 10A = 95, then a = 7
Do you understand?

Equal ratio sequence {an}, a1 + A2 + a3 + A4 + A5 = 8,1 / (A1) + 1 / (A2) + 1 / (A3) + 1 / (A4) + 1 / (A5) = 2, find A3. (the numbers after a are subscripts, which are serial numbers)

a1+a2+a3+a4+a5=8.A
a1+a2+a4+a5=8-a3.B
a3^2=a1a5=a2a4.C
1/(a1)+1/(a2)+1/(a3)+1/(a4)+1/(a5)=2
a3^3(a1+a2+a4+a5)/a1a2a3a4a5=2.D
Substituting B and C into D leads to
a3^3(8-a3)/a3^5=2
8-a3=2a3^2
2a3^2+a3-8=0
a3=[-1±√65]/4

After 40 tons of a batch of goods have been transported away, the remaining goods are 16 tons less than the original 85%. How many tons of this batch of goods were there?

Suppose there were x tons,
x-40=x*85%-16
The solution is x = 160