Xiaohua plans to fold an equilateral triangle out of a rectangular piece of paper ABCD, and he first

I have almost forgotten the theorem, so I may have a lot of steps, Xiaohua is right, connect AP, because GP=PH, AP is perpendicular GH, so, triangle AGP=triangle APH=triangle ADG, so, the angle GAH is 60 degrees, and the other two angles are also 60 degrees, so congruence, here is an ancient story of Einstein's origami trisecting right angles, Xiaohua is so powerful.

It is a regular triangle.

D folds onto EF so that AD coincides with AP, i.e. AD=APEF is the midline of the rectangle, so DP=AD=AP

The triangle ADP is a regular triangle.

dag=30°

gah=60°

agh=60°

So is AGH an equilateral triangle.

The triangle AGH is an equilateral triangle.

If the AP triangle APH and the triangle AGP(SAS) congruence are contoured, then AG=AH

Because dag= gap= pah

So gah is equal to 60 degrees.

And because ag=ah

So it's a regular triangle.

Another way.

Fold A and B C in half with D and crease EF

Then fold along the diagonal cf.

Finally, a regular triangle FCD is formed in the middle

First, according to the nature of the change of the ruler and the space of the figure, ade a de, aed= a ed, ade= a return limb de, and then according to the inner angle of the triangle and theorem, the degrees of aed+ ade and a ed+ a de are obtained, and then the answer can be found according to the nature of the flat angle

Answer: Solution: A de is a transformation of ABC folding, aed= a ed, ade= a de, a= a =75°, aed+ ade= a ed+ a de=180°-75°=105°, 1+ 2=360°-2 105°=150°

If it helps you, please give a good review.

It's not easy to answer the questions and needs your support.

If you don't understand something, please ask a question on the new page.

A de is a conversion of ABC folding.

aed=∠a′ed，∠ade=∠a′de，∠a=∠a′=75°。

aed+∠ade=∠a′ed+∠a′de=180°-75°=105°。

Nature of triangular angles:

1. The sum of the internal angles of the triangle on a plane is equal to 180° (the sum of internal angles theorem).

2. The sum of the outer angles of the triangle on the plane is equal to 360° (the sum of the outer angles theorem).

3. On the plane, the outer angles of the triangle are equal to the sum of the two inner angles that are not adjacent to it.

4. There are at least two acute angles in the three inner angles of a triangle.

5. At least one angle in the triangle is greater than or equal to 60 degrees, and at least one angle is less than or equal to 60 degrees.

6. In a right-angled triangle, if an angle is equal to 30 degrees, then the right-angled side opposite by the 30-degree angle is half of the hypotenuse.

aed+∠ade=180°-∠a=110°

dea'=aed, then ade= eda'Sun Mo key.

So dea'Maling + EDA'=110°

A rectangle can be spelled out using the following steps:

Combine two rectangles with side length A into a square, and the side length is hidden into 2A.

Assemble three rectangles with B sides into a 3B side.

Assemble five rectangles with sides of a and b to form a bar with a side length of 5a, and put them together with the rectangle in step 2 to obtain a rectangle with a side length of 5a and a width of 2b.

The square in step 1 is cut diagonally into two right-angled triangles, one of the triangles is rotated 180 degrees and the other triangle is put together to obtain a square with a side length of 2a and a width of 2a.

Cut the square in step 4 diagonally into two right-angled triangles, rotate one of the triangles 90 degrees and put together the other triangle to obtain a rectangle with a side length of 4a and a width of 2a.

Combine the rectangle in step 5 with the rectangle in step 3 to get a rectangle with a side length of 5a and a width of 4b.

Therefore, you can use 2 rectangles with side length a, 3 rectangles with side length b, and 5 rectangular pieces of paper with side length a and b to spell out a rectangle with a side length and a width of 4b.

A de is formed by the fold transformation of the cautious staring ade, aed= a hail filial piety ed, ade= a de, a= a =75, aed+ yuanzhi ade= a ed+ a de=180-75=105, 1+ 2=360-2 105=150

The answer is: A+2B

Untie; The area of 3 square pieces of paper with a side length is 3A2, the area of 4 rectangular pieces of paper with a side length and B (B A) is 4AB, and the area of 5 square pieces of paper with a side length B is 5B2, A2+4AB+4B2=(A+2B)2, and the longest side length of the square can be (A+2B),

Select C angle eda = angle 2 angle aed = angle 1 angle a = 75 degrees triangle dust respectful shape aed = 180 degrees angle 1 plus do zhi angle 2 = angle aed plus angle pure brother elimination eda is equal to 180 minus 75 = 105