Which statement is true for all regular pyramids?
A) the length of the altitude is equal to the length of the slant height***
B) all lateral faces are congruent isosceles triangles
C) the base and the faces are similar polygons
D) all edges are equal in lenght
No, slant height is hypotenuse of triangle where altitude is one leg and half the base is the other.
Nope.
http://www.mathsisfun.com/geometry/pyramids.html
is it B
Yes. B.
I guess b
To determine which statement is true for all regular pyramids, we need to understand the properties of regular pyramids.
A regular pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that converge to a single point called the apex or vertex. The base of a regular pyramid is a regular polygon, meaning that all its sides and angles are equal.
Let's analyze each statement:
A) The length of the altitude is equal to the length of the slant height:
The slant height of a pyramid is the length of the line segment connecting the apex to any point on the perimeter of the base. The altitude of a pyramid is the length of the perpendicular segment from the apex to the base, passing through the center of the base.
For a regular pyramid, the altitude is always shorter than the slant height. Therefore, statement A is false.
B) All lateral faces are congruent isosceles triangles:
The lateral faces of a regular pyramid are the triangular faces that are not part of the base. Since the base of a regular pyramid is a regular polygon, all its lateral faces are congruent isosceles triangles. Thus, statement B is true for all regular pyramids.
C) The base and the faces are similar polygons:
For a regular pyramid, the base and the faces are similar polygons. This means that the shape of the base is identical to the shape of each lateral face. Therefore, statement C is true for all regular pyramids.
D) All edges are equal in length:
Since a regular pyramid has a regular polygon as its base, all the sides of the base are equal in length. However, the edges connecting the apex to the vertices of the base are not equal in length. Therefore, statement D is false.
In conclusion, the statement that is true for all regular pyramids is:
B) All lateral faces are congruent isosceles triangles.