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Geometry scrapbook

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Geometry scrapbook - Page Text Content

1: Polygons : p. 2-3 Circles and Arcs : p. 4-5 Statements and truth values : p. 6-7 Conditional/biconditional statements : p.8-10 Midpoints : p. 11 Planes, points, and lines : p. 12-15 Angles : p. 16-20 | I remember when... | Riazul Alam

2: Polygons | Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have. The most familiar polygons are the triangle, the rectangle, and the square. A regular polygon is one that has equal sides. Polygons also have diagonals, which are segments that join two vertices and are not sides.

4: Circles | A circle is a set of points which are all a certain distance from a fixed point known as the center. A line joining the center of a circle to any of the points on the circle is known as a radius. The circumference of a circle is the length of the circle.

5: Through a study of the core curriculum, students in the Honors Program this year had the opportunity to view the connections among distinct subjects | This year our group of six top students had the honor of being invited to Washington D.C. for a special summit on the environment. | Arcs | An arc is a portion of the circumference of a circle.

6: Statements and Truth Values | A mathematical sentence is a sentence that states a fact or contains a complete idea. A sentence that can be judged to be true or false is called a statement , or a closed sentence.

7: Negation: -Indicates the opposite, usually employing the word not. The symbol to indicate negation is : ~ Conjunction: -In logic, a conjunction is a compound sentence formed by using the word and to join two simple sentences. The symbol for this is ^(whenever you see ^ read 'and') When two simple sentences, p and q, are joined in a conjunction statement, the conjunction is expressed symbolically as p^q. Disjunction: -In logic, a disjunction is a compound sentence formed by using the word or to join two simple sentences. The symbol for this is v (whenever you see v read 'or') When two simple sentences, p and q, are joined in a disjunction statement, the disjunction is expressed symbolically as p v q.

8: Conditional statements | A conditional statement, symbolized by pq, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion.

9: -The converse of a conditional statement is formed by interchanging the hypothesis and conclusion of the original statement.In other words, the parts of the sentence change places.The words "if" and "then" do not move. -The inverse of a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement.In other words, the word "not" is added to both parts of the sentence. -The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. In other words, the contrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE.

10: The Honors Program is designed to cultivate the talents, interests and scholastic aptitude of its students through an interdisciplinary approach to academic study. | Biconditionals | In logic, a biconditional is a compound statement formed by combining two conditionals under "and." Biconditionals are true when both statements (facts) have the exact same truth value. A biconditional is read as "[some fact] if and only if [another fact]" and is true when the truth values of both facts are exactly the same BOTH TRUE or BOTH FALSE.

11: In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. | Midpoints

12: Planes | In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or a parallelogram. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points.

13: The school spirit was nothing short of palpable all year. Our hearts and minds were in the game, and we stayed focused at every turn. | Points | In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. Our dot can be very tiny or very large and it still represents a point. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y).

14: Lines | In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. Unless otherwise stated a line is drawn as a straight line with two arrowheads indicating that the line extends without end in both directions. A line is named by a single lowercase letter, or by any two points on the line.

15: Collinear Points:points that lie on the same line. Coplanar points:points that lie in the same plane. Opposite rays:2 rays that lie on the same line, with a common endpoint and no other points in common. Opposite rays form a straight line and/or a straight angle (180:). Parallel lines:two coplanar lines that do not intersect Skew lines:two non-coplanar lines that do not intersect.

16: Angles | In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angle is also used to designate the measure of an angle or of a rotation.

17: Acute angles | An angle whose measure is less than 90 degrees. | Right angles | An angle whose measure is 90 degrees.

18: Obtuse angles | An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees. | Straight angles | An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line.

19: Reflex angles | An angle whose measure is bigger than 180 degrees but less than 360 degrees. | Adjacent angles | Angle with a common vertex and one common side.

20: Complementary angles | Two angles whose measures add to 90 degrees. Two angles do not have to be adjacent to be complementary as long as they add up to 90 degrees. | Supplementary angles

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  • By: Riazul A.
  • Joined: almost 6 years ago
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  • Title: Geometry scrapbook
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  • Published: almost 6 years ago