Lincoln Public Schools Math 8 McDougall Littell Middle School Math
... Items marked A, B, C are increasing in difficulty. Group “A” questions are the most basic while Group “C” are the most difficult and require higher levels of thinking skills. The level of difficulty is only relative to the same section. Most problems include random number generation within indiv ...
... Items marked A, B, C are increasing in difficulty. Group “A” questions are the most basic while Group “C” are the most difficult and require higher levels of thinking skills. The level of difficulty is only relative to the same section. Most problems include random number generation within indiv ...
Parallel Lines and Angle Relationships
... Mention that if two lines (or line segments or rays) are in different planes, they may be neither intersecting nor parallel. For example, an east-west line on the floor and a north-south line on the ceiling never meet, but they are not parallel either. These lines are called skew. Ask the class whic ...
... Mention that if two lines (or line segments or rays) are in different planes, they may be neither intersecting nor parallel. For example, an east-west line on the floor and a north-south line on the ceiling never meet, but they are not parallel either. These lines are called skew. Ask the class whic ...
TOPIC 11
... The figure has to be bounded by line segments (but the segments do not all have to be congruent), and the line segments can only intersect at their endpoints. The figure must be closed. (There has to be an interior and an exterior? How do we know which is the interior?) Only two segments can i ...
... The figure has to be bounded by line segments (but the segments do not all have to be congruent), and the line segments can only intersect at their endpoints. The figure must be closed. (There has to be an interior and an exterior? How do we know which is the interior?) Only two segments can i ...
Compass-and-straightedge construction
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass, see compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates. Every point constructible using straightedge and compass may be constructed using compass alone.The ancient Greek mathematicians first conceived compass-and-straightedge constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in some cases were unable to do so. Gauss showed that some polygons are constructible but that most are not. Some of the most famous straightedge-and-compass problems were proven impossible by Pierre Wantzel in 1837, using the mathematical theory of fields.In spite of existing proofs of impossibility, some persist in trying to solve these problems. Many of these problems are easily solvable provided that other geometric transformations are allowed: for example, doubling the cube is possible using geometric constructions, but not possible using straightedge and compass alone.In terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number. A number is constructible if and only if it can be written using the four basic arithmetic operations and the extraction of square roots but of no higher-order roots.