Math Forum: Ask Dr. Math FAQ: Defining Geometric Figures
faces meet at edges which are line segments and the edges meet at a point called .. A vertex of a polyhedron is a point where three or more edges meet. The face that is If actual distance between two places A and B is km and it is. A two-dimensional figure, also called a plane or planar figure, is a set of line segments or These points are zero-dimensional, but they also lie in the plane, which is two-dimensional. If all the edges are segments, every vertex is the endpoint of two sides, and no two When two sides meet at a vertex, they form an angle. Learn to identify the faces, edges, and vertices of solid figures. An edge is the line segment where two faces meet. You can see by looking at this A vertex is a point where several planes meet in a point. The arrow here is.
Question Answer A solid that is bounded by polygons, called faces, that enclose a single region of space. Polyhedron The polygons that enclose the polyhedron Face A line segment formed by the intersection of two faces of a polyhedron. Edge A point where three or more edges of a polyhedron meet.
Specifying planes in three dimensions | Geometry (video) | Khan Academy
Vertex A polyhedron whose faces are all congruent regular polygons. Regular Polyhedron A polyhedron such that any two points on its surface can be connected by a line segment that lies entirely inside or on the polyhedron. Convex The intersection of a plane and a solid. Cross Section Five regular polyhedra, named after the Greek mathematician and philosopher Plato, including a regular tetrahedron, a cube, a regular octahedron, a regular dodecahedron, and a regular icosahedron.
Platonic Solids A polyhedron with four faces. Tetrahedron A polyhedron with eight faces.
Octahedron A polyhedron with twelve faces. Dodecahedron A polyhedron with twenty faces.
Proof: Segments tangent to circle from outside point are congruent (video) | Khan Academy
Icosahedron A polyhedron with two congruent faces, called bases, that lie in parallel planes. The other faces, called lateral faces, are parallelogram formed by connecting the corresponding vertices of the bases.
Prism On a prism, these are the faces that have only TWO of the same polygonal shape. That's a tangent line. They're going to intersect at a right angle. So radius, tangent line, they intersect at a right angle. We also know, since OB and OC are both radii, that they're both the length of the radius of the circle. So this side, right over here, let me do some new colors here, so this side is going to be congruent to that side.
And you can see that the hypotenuse of both circles is the same side, side OA, so of course, it is equal to itself. This is equal to itself. So we see triangle ABO and triangle ACO, they're both right triangles that have two sides in common, in particular, they both have a hypotenuse that are equal to each other and they both have a base, or a leg.
And we know from Hypotenuse-Leg Congruence that if you have two right triangles, where the hypotenuses are equal, and you have a leg that are equal, then the both triangles are going to be congruent.
And in that proof where we prove it, as well, the Pythagorean theorem tells us if you know two sides of a right triangle that determines what the third side is. So the third side, so length of AB is going to be the same thing as the length of AC.
Once again, it just comes out of, these are both right triangles, if two sides, if two corresponding sides of these two right triangles are congruent, then the third side has to, that comes straight from the Pythagorean theorem. And there you go. The most common three-dimensional figures have only a few faces, the surfaces are very simple, and there are no "loose ends" - that is, every vertex is the end of at least two edges, and at least two faces meet at every edge.
If all the faces are plane regions, every edge is the edge of two faces, every vertex is the vertex of at least three faces, and no two faces cross each other, the figure is called a polyhedron.
Here are some names of polyhedra. Polyhedra often divide space into two pieces, an inside and an outside. The name of the figure is also commonly used for this region, and the volume of the region is commonly called the volume of the figure.
When two planar faces come together at an edge, they form an angle.
Specifying planes in three dimensions
The one inside is called the dihedral angle dihedral means "having two faces" at that edge, or simply the angle at that edge. Mathematically speaking, a tetrahedron consists of four triangular faces, six edges, and four vertices only. When you want to refer specifically to the interior of a figure that does not have a name of its own, you can call it "the region of space enclosed by the figure" or the figurate solid: A note on dimensions A point, which is 0-dimensional, can lie on a line, in a plane, or in space.
A line, which is 1-dimensional, can lie in a plane or in space. A plane, which is 2-dimensional, can lie in space, and space is 3-dimensional.