Ad bisector ∠ BAC, the vertical bisector of ad intersects the extension line of BC with point E, intersects ad with point F, and proves ∠ EAC = ∠ B Use the vertical bisector of a line segment

Ad bisector ∠ BAC, the vertical bisector of ad intersects the extension line of BC with point E, intersects ad with point F, and proves ∠ EAC = ∠ B Use the vertical bisector of a line segment

Proof: it can be seen from the figure that: ∠ ECA = ∠ CAD + ∠ EDA, ∠ EAB = ∠ bad + ∠ ead,
∵ ad bisection ∠ BAC, ∵ CAD = ∠ bad,
If ∵ EF vertical bisection ad ∵ ead is isosceles triangle, then ∵ EDA = ∵ EAD
∴∠ECA=∠EAB
And ∵ ∠ CEA = ∠ AEB
∴△EAC∽△AEB
∴∠EAC=∠B

The four sides of the solid figure V ~ ABC are congruent regular triangle lines. Draw the plane angle of the dihedral angle V ~ AB ~ C and find its degree

Take the midpoint D of AB, then the angle VOC is the plane angle of the dihedral angle V ~ AB ~ C. It is proved that the triangles can be combined into one
Obviously, the triangle VOC is also an equilateral triangle, so the angle VOC is 60 degrees
So the degree of dihedral angle V ~ AB ~ C is 60 degrees

How to draw the plane angle of a dihedral angle in a graph, that is, how to add auxiliary lines

Find the common edge of two faces, and then in one face, take a point a in the face as the starting point to make the vertical line of the common edge, set intersection common edge and e point, take a point as the vertical line of the other face, intersection the other face and F, connect ef, then the plane angle AEF of dihedral angle is made

Cosine of dihedral angle formed by any two adjacent faces of octahedron!