Triangle Inequalities
Triangles are governed by two important inequalities. The first is often referred to as the triangle
inequality. It states that the length of a side of a triangle is always less
Pyramids and Cones
Pyramids
Another interesting kind of polyhedron is a pyramid. A pyramid is the union of a polygon with
all of the segments that have one endpoint on the polygon and the other endpoi
Declarative Sentences
As the Introduction said, geometry consists of numerous declarative sentences. A declarative
sentence is a sentence that asserts the truth or falsehood of something. For example,
Deductive and Inductive Reasoning
Using proofs, you could measure one figure or part of a figure and know the measure of another
figure or part of that figure which is impossible to measure. Naturally
Terms
Altitude of a Cone - The segment with one endpoint at the vertex of a cone and the other
in the plane that contains the base of the cone.
Altitude of a Pyramid - The segment with one endpoint at
The Structure of a Proof
Geometric proofs can be written in one of two ways: two columns, or a paragraph. A paragraph
proof is only a two-column proof written in sentences. However, since it is easier
Corresponding Parts of Triangles
To prove that two triangles have the same shape, certain parts of one triangle must coincide with
certain parts of the other triangle. Specifically, the vertices of ea
Constructing Figures
When points, lines, and planes are put together, they form more complex geometric shapes. In
basically every geometric figure that we'll study, angles are formed between lines, se
Building Block of Geometry
Geometry is essentially the study of shapes. In the world around us, every object we see is a
shape of some kind. Some are simple, like a triangle, square, or circle. Others
Measurements in Three Dimensions
In Geometry 1, we were introduced to the idea of three-dimensional surfaces. We chiefly studied
simple closed surfaces and, more specifically, polyhedrons. Remember, p