Geometry scrapbook Meta Thurman
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The document is Meta Thurman's scrapbook from November 19th 2012. It discusses various geometry concepts like parallel lines, congruent objects, vertical angles, perpendicular lines, intersecting lines, supplementary angles, different proportions, adjacent angles, similarity, 2D and 3D shapes, surface area, Pythagorean theorem, diameter, and volume. Many of the concepts are related to diagrams of horses, fences, and tack for horseback riding to explain their practical applications.
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This document defines and provides examples of various types of lines and angles in geometry. It begins with defining basic terms like points, lines, line segments, rays, intersecting and non-intersecting lines. It then defines different types of angles like acute, right, obtuse, straight, reflex, adjacent and vertically opposite angles. Finally, it discusses parallel lines and the angles formed when lines are cut by a transversal, including corresponding angles, alternate interior angles, and interior angles on the same side of the transversal.
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- Solid shapes such as cubes, cylinders, and cones and their defining characteristics
- Lines, angles, and their classifications
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- Properties of triangles, quadrilaterals, and other shapes
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Symmetry is seen in many areas of mathematics and comes in several types. Reflectional symmetry, or line symmetry, occurs when one half of a figure is a mirror image of the other half across a central line. Rotational symmetry exists when a figure can be rotated around a central point and overlap itself, with the smallest angle of rotation determining its order of symmetry. Point symmetry exists when every part of a figure has a matching part the same distance from the central point but in the opposite direction.
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The document provides an introduction to a math class on parallel lines and lines intersected by a transversal. It includes examples of parallel lines in real life, definitions of key terms like parallel planes, transversals, and the different types of angles formed when parallel lines are cut by a transversal. Students are instructed to identify examples of parallel lines in and outside the classroom and discuss how parallelism appears in daily life. The lesson concludes with exercises coloring examples, classifying angles, and measuring angles to reinforce the concepts learned.
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This document provides information about 2D shapes for a 3rd grade math lesson, including definitions and examples of points, lines, line segments, rays, angles, and various polygons. It defines right, acute, and obtuse angles. It also defines and provides examples of parallel, perpendicular, and intersecting lines. Finally, it defines and provides examples of common polygons like triangles, quadrilaterals, pentagons, hexagons, and octagons.
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This document defines and describes several geometric shapes including linear pairs of angles, octagons, parallel lines, parallelograms, arcs, circles, trapezoids, and isosceles triangles. It provides brief definitions for each shape stating their key properties such as number of sides, angles, and relationships between sides or angles.
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The document defines important terms in 2D geometry including points, lines, planes, line segments, rays, angles, parallel and perpendicular lines, acute, right, and obtuse angles, polygons, triangles, quadrilaterals, and naming conventions for triangles and quadrilaterals based on their angle and side properties. Key shapes are defined such as the triangle, parallelogram, rectangle, square, rhombus, and their specific names depending on features like equal sides or right angles.
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This document discusses different types of angles and their relationships. It defines a ray, line, and line segment. When two lines intersect, they form four right angles. A transversal is a line that intersects two or more coplanar lines. When a transversal crosses parallel lines, it forms corresponding angles, alternate interior angles, and alternate exterior angles that are equal. Interior angles on the same side of the transversal are also congruent.
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This document defines and explains various angle types and angle relationships. It contains:
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Vocab lessons 7 1 through 7-5
- A point is named by a capital letter. A line is named by two points on the line. A plane is named by three non-collinear points.
- A line segment is named by its two endpoints. A ray has one endpoint and extends without end in one direction. An angle is named using the vertex in the middle and the two rays.
- Angles are measured and can be acute, right, or obtuse. A protractor is used to measure angles. Vertical angles, adjacent angles, complementary angles, and supplementary angles are special angle relationships.
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Geometry scrapbook Meta Thurman
- 1. Meta’s scrapbook By Meta Thurman November 19th 2012
- 2. Table of Contents
- 3. Parallel Lines Parallel lines are lines that will never intersect, and will stay the same distance apart no matter how long the lines are. If these lines were not parallel the horse would fall over. Also if the lines were not parallel that would mean the horse has alignment problems.
- 4. Congruent objects Congruent Objects are objects that are the same size. If the crossties weren’t congruent they would not fulfill all of their jobs. Not all of the tack would fit on the sides, not all the horses would fit, and the instructor couldn’t see all of her students appropriately.
- 5. Vertical Angles are angles that are opposite of each other when two lines cross. These vertical angles help keep the fence up. If the fence wasn’t up it would be easy for the horses to run away with in- experienced riders who have less control. Vertical Angles
- 6. Perpendicular Lines Perpendicular lines are lines that intersect and create a 90 degree angle. These perpendicular lines are necessary because if they weren’t the gate wouldn’t work. If the gate didn’t work the horses either couldn’t get in or couldn’t get out of the arena.
- 7. Intersecting Lines Intersecting lines are lines that have only one point in common. In this picture the cross rail is the source of the intersecting lines. These lines must intersect because if they didn’t there wouldn’t be any variation of jumps and difficulty.
- 8. Supplementary Angles Supplementary angles are two or more angles that add up to a total of 180 degrees. This breast plate has supplementary angles to help keep it on the horse. If the breast plate didn’t have these angles it wouldn’t keep the saddle from slipping back.
- 9. Different Proportions Different Proportions means that two things of the same kind are different sizes. These horses are different proportions because they are different breeds. It is important that these are of different proportions because there must be different sizes for different sized people.
- 10. Adjacent Adjacent angles are angles that have a common vertex but do not overlap.
- 11. Similarity Similarity means that two objects have the same shape.
- 12. 2 dimensional Two Dimensional means that the object only has two dimensions (length and width)
- 13. Surface area The Surface area of an object is the total area of the surface of a 3 dimensional object.
- 14. Pythagoras The Pythagorean theorem is the theorem attributed to Pythagoras that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse.
- 15. Diameter Diameter is a straight line going from side to side through the middle of a circle.
- 16. When an object is 3 dimensional it means the object has three dimensions (height, length, and width) 3 Dimensional
- 17. Volume Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.