S: MATH SCRAPBOOK
BC: Geometry Scrapbook | Jarred Stanford | Mrs. Peays Class
FC: Geometric Termoil | Jarred Stanford | Period:Second | Date:11/14/2012
1: Table of Contents | Title Page Table of contents:Page 1 Geometry Basics:Pages 2-3 Angles and their measures:Pages 4-5 Angles and Segment Bisectors:Pages 6-7 Complementary,Supplementary, and Vertical angles:Pages 8-9 Parallel Lines and Angles formed by transversals:Pages 10-11 Perpendicular Lines:Pages 12-13 Triangles (classifying, angle measurements, etc):Pages 14-15 Pythagorean Theorem and Distance Formula:Pages 16-17 Congruent Triangles (including the 5 ways to prove congruency):Pages 18-19 Polygons (Parallelograms, rhombuses, rectangles and squares):Pages 20-21 Geometric Terms of Choice: Pages 22-23
2: Finding and Describing Patterns | Diamond/Triangle/Diamond/Triangle | This is an example of a Visual Pattern | Geometry Basics | Real World Relation:
3: Points,Lines,and Planes | A point has no dimension. It is represented by a dot | A line has one dimension. It extends in two directions. It is represent by a line with two arrows | A plane has two dimensions. It is represented by a shape that looks like a floor or wall. | This picture represents 2 of 3. Point B, Point C and Point A are all Points. Plane M is a Plane. | Real World Relation: | The Outside lines are Lines | Segments and Their Measures | The real number that corresponds to a point is the coordinate. | A segment consist of endpoints. It is formed by a line with points on each side | Segment | Real World Relation
4: Angles and Their Measures | An Angle consist of two rays that have the same endpoint | The rays are the sides of the angle | The endpoint is the vertex of the angle | Acute: Measure is between 0 and 90 degrees | Obtuse: Measure is between 90 and 180 degrees | Right: Measure is 90 degrees | Straight: Measure is 180 degrees
5: EXAMPLE | Real World Relation:
6: Angles and Segment Bisectors | Definitions | A segment bisector is a segment,ray,line, or plane that intersects a segment at its midpoint. To bisect a segment means to divide the segment into two congruent segments | An Angle Bisector is a ray that divides an angle into two angles that are congruent.
7: Segment Bisector | In this photo the 2 Highlighted hands of the clock are shown easily. In the middle of these hands is another faded line. This is a real life example of a angle bisector. | Segment OE bisects Segment JN with the midpoint S | In this photo Ray BD bisects Angle ABC.
8: Complementary, Supplementary, and Vertical Angles | Definitions | Two angles are complementary angles if the sum of their | measures adds up to 90 degrees. | Two angles are supplementary angles if the sum of their | measures adds up to 180 degrees. | Two angles are vertical angles if they are not adjacent and | their sides are formed by two intersecting lines.
9: Real example of a supplementary angle
10: DefINITIONS | Parallel Lines and Angles formed by transversals | Two lines are parallel lines in the same plane and do not intersect | A transversal is a line that intersects two or more coplanar lines at different points. | Corresponding: Two angles are corresponding angles if they occupy corresponding positions. | Alternate interior: Two angles are alternate interior angles if they lie in between the two lines on the opposite sides of the transversal | Alternate Exterior: Two angles are alternate exterior angles if they lie outside the two lines on the opposite sides of the transversal | Same-Side interior: Two angles are same side interior angles if they lie between the two lines on the same side of the transversal.
11: Pictures | Angle 2 and Angle 6 are corresponding angles. Angle 4 and Angle 5 are alternate interior angles. Angle 1 and Angle 8 are alternate exterior angles. Angle 3 and Angle 5 are same-side interior angles.
12: All right angles are congruent. | Definition of Perpendicular Lines | If two lines are perpendicular, then they intersect to form four right angles. | If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. | In a plane, if two lines are perpendicular to the same line, then they are parallel to each other . | A converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion
13: Perpendicular Lines | Perpendicular lines form 90 degree angles. | Real World Example Tennis Lines
14: Definition of Triangles, Angle measures, Names of Triangles | A triangle is a figure formed by three segments joining three non-collinear points. A triangle can be classified by its sides and by its angles. | Equilateral triangle-3 congruent sides Isosceles Triangle-At least 2 congruent sides Scalene triangle-No congruent sides | Equiangular Triangle-3 congruent angles Acute triangle-3 acute angles Right triangle-1 right angle Obtuse triangle-1 obtuse angle | A vertex of a triangle is a point that joins two sides of the triangle. The side across from an angle is the opposite angle | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles | If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then it equilateral
15: Pictures | Definitions of triangles,Angle measures,Names of triangle picture examples and real world examples
16: PythagoRean Theorem | aND | Distance Formula | In a right triangle, the sides that form the right angle are called legs THe side opposite the right angle is called the hypotenuse. (a2+b2=c2) | If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is A B\/'''''''''''''''''''''''''''''''''' (x2-x1)2+(y2-y1)2
17: Pictures | Pythagorean Theorem and Distance formula pictures, examples, and real life relations.
18: Congruent Triangles | Corresponding angles and corresponding sides are examples of Corresponding Parts | Figures are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent | SSS: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent | 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 | 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 | 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 | HL: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent
20: Polygons Parallelograms, Rhombuses, Rectangles and Squares | A polygon is a plane figure that is formed by three or more segments called sides . Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon. | A segment that joins two nonconsecutive vertices of a polygon is called a diagonal . | A parallelogram is a quadrilateral with both pairs of opposite sides parallel. | A rhombus 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. | A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases . The nonparallel sides are the legs . | If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid .
22: Definitions | The centroid of a triangle is the point where the three medians meet. This point is the center of mass for the triangle. | The intersection of two or more figures is the point or points that figures have in common. | A construction is a geometric drawing that uses a limited set of tool., usually a compass and a straightedge is a ruler without marks. | A Polygon with 5 sides is called a pentagon. | A 6 SIDEd Polygon is called a hexagon. | A 7 sided Polygon is called a heptagon | A 8 sided Polygon is called an Octagon. | A line of symmetry is a line of reflection. | A reflection is a transformation that creates a mirror image. | A segment,ray,or line that is perpendicular to a segment at its midpoint is called a perpendicular bisector.