Can a triangular pyramid be a right triangle on all four sides?

Yes, the triangular pyramid can be a right triangle on all four sides.

In a triangular pyramid V-ABC, the side edge va is the bottom surface of abc, and b in abc is a right angle, then it can be seen that all four sides of the triangular pyramid are right-angled triangles, so that the conclusion can be obtained.

Solution: If a triangular pyramid is V-ABC, the side edge VA is on the bottom of ABC, and ABC is at a right angle.

Because BC is perpendicular to the projection of VA.

AB, so VA is perpendicular to the diagonal line VB of the plane ABC, so VBC is at right angles.

By the va bottom surface abc, so vab, vac are all right angles.

Thus the four faces of the triangular pyramid are abc; ∠vab；∠vac；VBC are all right angles.

So the triangular pyramid is a right triangle on up to four sides.

1. Yes.

2. (1) You can imagine with a corner, the two faces on the two walls must be right-angled triangles, and the faces on the floor are also right-angled triangles, so you only need to determine another face, you can first determine an edge, and then take an edge perpendicular to it, so that this surface is also a right-angled triangle.

2) Observing the three views, it can be seen that the bottom surface of the triangular pyramid is <>

It is a right triangle and <>

Side <>

It is a right triangle and <>By <>

Knowing <> "Side <>

It is also a right-angled triangle, so the <> is chosen

Not necessarily. Reason: The sides of the regular quadrangular pyramid are equilateral triangles only if the length of the bottom side of the pyramid is equal to the length of the edge.

Brief introduction to the regular quadrangular pyramid: the base is square, and the sides are 4 congruent isosceles triangles.

And there are common vertices.

The properties of the regular quadrangular pyramid are exemplified as follows:1. The edges on each side are equal, and each side is an isosceles triangle that is congruent, and the height on the bottom edge of each isosceles triangle is equal.

2. The projection of height, oblique height and oblique height in the bottom surface forms a right-angled triangle.

The projection of the height, side edge and side edge of the regular pyramid in the bottom surface also forms a permeable right triangle;

3. Raise the corners formed by the side edges and the bottom surface. Equal.

It's okay to laugh.

According to the Qingxia Education inquiry, if a triangular pyramid V-ABC, the side edge VA is the bottom of the ABC, and the ABC B is a right angle.

Because the BC is perpendicular to the va's shot and shadow AB, the VA is perpendicular to the diagonal line VB of the plane ABC, so the VBC is at right angles.

By the va bottom surface abc, so vab, vac are all right angles, so the four sides of the triangular pyramid abc, vab, vac, vbc are all right angles.

Therefore, the triangular pyramid can be a right-angled triangle on up to four sides, so the three sides of the triangular pyramid can be right-angled.

The four sides of the triangular pyramid collapse at most have three right-angled triangles to prove it: the bottom of the shilling is a straight or angular triangle, and the two right-angled sides of the right-angled triangle are the right-angled sides of the two sides respectively (i.e., the three sides are in the shape of wall angles).If the third side is still a right-angled triangle (first of all, it is determined that the top angle cannot be a right angle), then its two.

Let a positive n pyramid be much higher than the bottom edge, and the edge length must be much larger than the bottom edge.

Now gradually move the vertices of the pyramid towards the ground, so that the height gradually decreases, and the side edges of the pyramid also gradually decrease.

When the vertex and the bottom center coincide, the side edge becomes the radius of the circumscribed circle on the bottom surface.

In this process, the change in the length of the side edges is continuous.

So the question becomes: is it possible that the side edge is equal to the bottom edge 1 and 2 times the number in this change process.

Obviously, the beginning of the edge length l is much longer than the length of the bottom edge, and the length of l>>s>s root number 2 is when it coincides with the bottom surface.

l' =s/2) *sin(pi/n)

Therefore, when 2sin(pi n) > root number 2, the morning song is established, that is, sin(pi Lu Zheng n)> root number 2 2 is established.

Apparently n can only be 3

How many right triangles are there at most of the four faces of a triangular pyramid? and give reasons.

Hello old Kaiye, I am milk pudding 9696, the answer in the field of education, I am very happy to answer your question, I have received your question, the four sides of a triangular pyramid have a maximum of several right trianglesThe answer is as follows: The four sides of the triangular pyramid have a maximum of 3 right triangles Proven: the bottom of the shilling is a right triangle, and the first right angle side of the two grandsons of the right triangle is the right angle side of the two sides (that is, the three sides are in the shape of a wall corner).

If the third side is still a right triangle (first of all, the top angle cannot be a right angle), then one of its two sides must be a right angle, then one of the sides must be perpendicular to both sides that intersect it, and if this is the case, then it is not a triangular pyramid, that is, four faces that cannot be sealed.

Yes, the sides of the regular triangular pyramid are regular triangles.

A regular pyramid is a polyhedron with four faces, three of which are equilateral triangles, called sides, and the fourth is the base. Each side is a regular triangle made up of three sides, where the three sides are equal in length and at equal angles.

Therefore, each side of the triangular pyramid is a regular triangle. Lu Zhaocoar.

No conditions were given.

If the regular triangular pyramid p-abc, the edge length of the bottom triangle is a, and the side edge length is b, then the vertex p projection o on the bottom surface is the outer center of the regular triangle (center of gravity, inner center, vertical center), oa = ( 3 2) a * (2 3) = 3a 3, according to the Pythagorean theorem failure chain collision, high op = (pa 2-oa 2) = b 2-a 2 3) = (1 3) ( 9b 2-3a 2)

Note that this is not a regular tetrahedron, the side and bottom edges are not the same length, and the distance from the center of gravity to the vertex is 2 3 of the length of the midline, according to the nature of the center of gravity.

Not necessarily. Reason: Only when the length of the bottom side of the pyramid is equal to the length of the edge, the side of the pyramid is equilateral.

Brief introduction to a regular quadrangular pyramid: The base is a square, and the sides are 4 congruent isosceles triangles with common vertices.

The properties of the regular quadrangular pyramid are exemplified as follows:1. The edges on each side are equal, and each side is a congruent isosceles triangle, and the acre limb height on the bottom edge of each isosceles triangle is equal;

2. The projection of height, oblique height and oblique height in the bottom surface forms a right-angled triangle, and the projection of the height, side edge and side edge of the positive pyramid in the bottom surface also forms a right-angled triangle;

3. The angles formed by the side edges and the bottom surface are equal.

If the bottom surface of a pyramid is a positive multi-swim front edge, and the projection of the vertex on the bottom surface is the center of the bottom surface, such a pyramid is called a regular pyramid.

Properties of the pyramid (1) The sides of the pyramid are equal, and each side is a congruent isosceles triangle, and the height on the bottom edge of the isosceles triangle is equal (it is called the oblique height of the pyramid); 2) The projection of the height, oblique height and oblique height of the positive pyramid in the bottom surface forms a right-angled triangle of Senpin, and the projection of the height, side edge and side edge of the positive pyramid in the bottom surface also forms a right-angled triangle; (3) The angles formed by the side edges of the regular pyramid and the bottom surface are equal; The dihedral angles formed by the side and bottom of the pyramid are equal; (4) The side area of the pyramid: If the circumference of the bottom surface of the pyramid is c and the oblique height is h', then its side area is s=1 2ch