Solving! Mathematical Geometry Solid Geometry Solution!

After watching it for a long time, I finally admitted that I had returned my geometry knowledge to the teacher.

Let's give you some ideas, connect AP, BP, CP to try.

Let me ask you to answer your questions.

First question: You can prove the ABC first

All equals EFC(ac=fc,bc=ec, acb= ecf, because acb+ ace= ecf+ ace, so acb= ecf).

Then ab=ef=ad

The same can be said af=de

then adef is.

Parallelogram.

The second question is when eda=90°.

Then edb = 150° = bac ( edb is equal to cab).

Then the answer is when the apex angle of the abc is 150°.

The quadrilateral is rectangular.

The third question is when the daf is collinear.

Then the first case.

Absent at bac=60°.

In the second case, when d and f coincide.

bac=240°, and this degree is greater than the sum of the inner angles of the triangle, then the answer is when bac=60°.

Hope it helps.

Give me some time.

We've done that.

But that's the first.

We don't need to prove the second and third questions.

Proof: Positive EBC

BC=EC positive AFC

ac=fc∠ace+∠ecf=60°

acb+∠ace=60°

acb=∠ecf

abc≌△afc

ab=ad=ef

The same can be said for EDB ABC

fa=ac=fa

Quadrilateral DAFE is a parallelogram.

Second: When bac=90°, it is a rectangle.

Thirdly: BAC=60°, does not exist.

2.Cross the point M as a BC parallel line, and cross AB at the point E

Because m is the midpoint of cd, e is the midpoint of ab.

And because AB is vertical BC, so ME AB

So me is the middle perpendicular line of the line segment AB.

So ma=mb

So mab= mba

3.Let the acute angle of the parallelogram be a

then the long side sina=3

Short side sina=2

So the long side: the short side = 3:2

So the long side is.

So the area is 15

4.Translate the diagonal line, convert the trapezoidal area to a triangle with side lengths of 3, 4, and 5, and determine that it is a right triangle according to the inverse theorem of the Pythagorean theorem.

The area is 3 4 2 = 6

5.Be cd, AF cd respectively

then af=be=ce=3 2 14, ef=ab=5df=1 2 42

So cd=ce+ef+df=3 2 14+5+1 2 42

The radius of the circumscribed circle r is c, and the area is s

There is s=c*r 2

Since abc is an isosceles triangle, it is easy to find the height on the bottom edge as 12, so the area s=12*10 2=60

c＝13+13+10＝36

So r=2s, c=2*60, 36=10, 3

The dihedral angle is generally solved by the coordinate system method, and the dihedral angle is calculated by using the method that the cosine value of the angle between the normal vectors is equal to the cosine value of the dihedral angle.