FC: GEOMETRY | F O R | FRESHMEN | Shelby Lawless 2nd Period December 12, 2012
1: Table of Contents | Page 1: Table Of Contents Pages 2-3: Chapter One Basics Pages 4-5: Angles and Their Measures Pages 6-7: Angle and Segment Bisectors Pages 8-9: More About Angles Pages 10-11: Parallel Lines and Angles formed by transversals Pages 12-13: Perpendicular Lines Pages 14-15: Triangles Pages 16-17: Pythagorean Theorem and Distance Formula Pages 18-19: Congruent Triangles Pages 20-21: Polygons
2: Chapter One Basics | Patterns can be predicted. A conjecture is an unproven statement that is based on a pattern or observation. Making a conjecture is called inductive reasoning. | A point has no definition. | A line has one dimension. It extends without end in two directions. | A plane has two dimensions it is represented by a shape that looks like a floor or wall. | Line Examples
3: Chapter One Basics | Point Examples | Pattern Examples | Plane Examples
4: Angles and Their Measures | An angle consists of two rays, that have the same endpoint, called the vertex. The measure of an angle is written in a unit called degrees. If angles are congruent, they have the same measure. Angles are classified as: right, 90 degrees; acute, between 0 and 90 degrees; obtuse, between 90 and 180; and straight, 180 degrees.
5: Obtuse | Straight | Right | Acute
6: Segment Bisectors | The midpoint of a segment is the point of the segment that divides it into two congruent segments. A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. When you bisect a segment, you cut it in half. | Midpoint | DE is a segment bisector.
7: Angle Bisectors | An angle bisector is a ray that divides an angle into two angles that are congruent.
8: More About Angles | Two angles are complementary angles if the sum of their measure is 90 degrees. Two angles are supplementary angles if the sum of their measures is 180 degrees.
9: Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines.
10: Lines are parallel lines if they lie on the same plane and are the same distance apart over their entire length
11: Angles formed by transversals are when two parallel lines are cut by a third line.
12: A line is perpendicular to another if they meet at 90 degrees. The two lines will form right angle at their intersection.
14: A triangle is a figure formed by three segments joining three noncollinear points called vertices. The sum of the measures of a triangle is 180 degrees | Triangles can be classified by sides Equlilateral Triangle - 3 congruent sides Isosceles Triangle - 2 congruent sides Scalene Triangle - No congruent sides
15: Triangles can be classified by angles Equilateral Triangle - 3 congruent angles Right Triangle - 1 right angle Acute Triangle - 3 acute angles Obtuse Triangle - 1 obtuse angle
16: The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
18: Congruent Triangles Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
19: Five ways to prove Triangles are Congruent Side-Side-Side (SSS) - if three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side-Angle-Side (SAS) - if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. Angle-Side-Angle (ASA) - if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Angle-Angle-Side (AAS) - if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. Hypotenuse-Leg (HL) - if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent.
20: A polygon is a plane figure that is formed by three or more sides and each side intersects exactly two other sides at each of its endpoints
21: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombuses is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles.