BC: The End
FC: The Geometry Scrapbook By Evelyn Turner 2nd Period December 12th, 2012
1: Table of Contents | Chapter 1: Pages 2-3: Geometry Basics Pages 4-5: Angles and their measures Chapter 2: Pages 6-7: Angle and Segment Bisectors Pages 8-9: Complementary, Supplementary, and Vertical Angles Chapter3: Pages 10-11: Parallel lines and angles formed by a transversal Pages 12-13: Perpendicular lines Chapter 4: Pages 14-15: Triangles Pages 16-17: Pythagorean Theorem and Distance Formula Chapter 5: Pages 18-19: Congruent Triangles Chapter 6: Pages 20-21: Polygons Extra Credit: Pages 22-23: Extra Credit
2: Chapter 1: Geometry Basics | A plane has two dimensions. It is represented by a shape that looks like a floor or wall. | An example of a plane is a wall or floor. | A real world example of planes is the walls in my room. | A plane
3: A point has no dimension. It is represented by a small dot. | A line has one dimension. It extends without end in two directions. It is represented by a line with two arrowheads. | A line | A point | An example of a line would be the lines on the middle of the road. | An example of a point is the period at the end of a sentence.
4: Angles and their measures | - Acute angles measure between 0-90 degrees. - Right angles measure 90 degrees. - Obtuse angles measure between 90-180 degrees. - Straight angles measure 180 degrees.
5: Acute angle | Right angle | Obtuse angle | Straight angle | An example of a angle is on a modern GPS route.
6: An angle bisector is a ray that divides an angle into two angles that are congruent. A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. | Chapter 2: Angle and Segment Bisectors
7: Angle Bisector | Segment Bisector | A real example of an angle bisector is a tent.
8: Complementary, Supplementary, and Vertical Angles | Two angles are complementary angles if the sum of their measures is 90 degrees. | Two angles are supplementary angles if the sum of their measures is 180 degrees. | Complementary Angles | Supplementary Angles
9: Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines. | Vertical Angles | A real world example of vertical angles is crossed snow skis.
10: Chapter | Parallel Lines and Angles Formed By a Transversal | Two lines are parallel lines if they lie in the same plane and do not intersect. | There are four types of angles that can occur because of a transversal. | Two angles are corresponding angles if they occupy corresponding positions. | Parallel Lines | A real world example of parallel lines is the yellow stripes on the road. | Corresponding Angles
11: Two angles are alternate interior angles if they lie between the two lines on the opposite sides of the transversal. | Two angles are alternate exterior angles if they lie outside the two lines on the opposite sides of the transversal. | Two angles are same-side interior angles if they lie between the two lines on the opposite sides of the transversal. | Alternate Interior Angles | Same-side Interior Angles | Alternate Exterior Angles | E and D
12: Perpendicular Lines | A real world example of perpendicular lines is the lines on a tennis court.
13: Two lines are perpendicular lines if they intersect to form a right angle.
14: Chapter 4: Triangles | A triangle is a figure formed by three segments joining three non-collinear points. | Triangle | A real world example of a triangle is Nabisco's logo. | An acute triangle has three acute angles. | An Equiangular triangle has three congruent angles. | Acute Triangle | Equiangular Triangle
15: A Equilateral triangle has three congruent sides. | An Isosceles triangle has at least two congruent sides. | A Scalene Triangle has no congruent sides. | A right triangle has one right angle. | An obtuse triangle has an obtuse angle. | Right Triangle | Obtuse Triangle
16: Pythagorean Theorem and the Distance Formula | 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. | Pythagorean Theorem | A real world example of the Pythagorean theorem is the height of a fire-fighter's ladder against a building.
17: Distance Formula: IfA (x1,y1) and B (x2,y2) are points in a coordinate plane, then the distance between A and B is AB= the square root of (x2-x1)to the second power + (y2-y1) to the second power. | Distance Formula
18: Chapter 5 | Chapter 5 | Proving Triangles are Congruent | ASA | Angle Side Angle: 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. | SSS | Side Side Side: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. | Side Angle Side: 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. | SAS
19: - Figures are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent. | AAS | Angle Angle Side: 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 | Hypotenuse-Leg: 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. | A real world example of congruent triangles are the Egyptian pyramids.
20: Chapter 6: | Polygons | A polygon is a plane figure that is formed by three or more segments called sides. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. | Polygon | Parallelogram | A real world example of a parallelogram is window panes.
21: 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 congruent angles. | Square | Rhombus
22: Extra Credit: | Coplanar Points are points that lie on the same plane. | Coplanar Lines are lines that lie on the same plane.
23: A conjecture is an unproven statement that is based on a pattern or observation. | Postulates are statements that are accepted without further justification. | Collinear Points are points that lie on the same line.