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Geometry Scrapbook

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Geometry Scrapbook - Page Text Content

S: Geometry Scrapbook

FC: Geometry Scrapbook | Hunter Galbraith 3rd Period 10/27/2012

1: Table of Contents | Pages 2-3: Chapter 1 Sections 1-5 Vocabulary Pages 4-5: Angles Pages 6-7: Angle and Segment Bisectors Pages 8-9: Complementary, Supplementary, and Vertical Angles Pages 10-11: Parallel Lines and Angles Formed by a Transferal Pages 12-13: Perpendicular Lines Pages 14-15: Triangles and Angle Measures Pages 16-17: Pythagorean Theorem and Distance Formula Pages18-19: Congruent Triangles Pages 20-21: Polygons | Pages 2-3: Chapter 1 Sections 1-5 Vocabulary Pages 4-5: Angles Pages 6-7: Angle and Segment Bisectors Pages 8-9: Complementary, Supplementary, and Vertical Angles Pages 10-11: Parallel Lines and Angles Formed by a Transferal Pages 12-13: Perpendicular Lines Pages 14-15: Triangles and Angle Measures Pages 16-17: Pythagorean Theorem and Distance Formula Pages18-19: Congruent Triangles Pages 20-21: Polygons

2: Chapter 1 Sections 1-5 Vocabulary | point- has no dimension; it is represented as a small dot | postulate- a statement that is accepted without further justification | This is Euclid's parallel lines postulate. | segment- a part of a figure cut off by a line or plane intersecting it.

3: plane- a flat surface on which a straight line joining any two points on it would wholly lie | intersection- a point at which two or more things intersect | Real World Example: A venn diagram is actually just two circles intersecting at two different points.

4: Angles | Angles are defined as the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line. | Real World Example: A yield sign is a triangle made up of three acute angles. | This is an acute angle.

5: Angles are measured in degrees. Angles are then classified according to their size. There are four different classifications depending on the measure of the angle's degrees. First there is the acute angle, an angle is classified acute if it is 0-89 degrees. Second is the right angle, an angle is classified as right if it is 90 degrees. Third is the obtuse angle, an angle is classified as obtuse when the angle measures to be 91-179 degrees. Finally an angle is also classified as a straight angle, an angle is classified as straight if it measures out to be 180 degrees.

6: Chapter 2 Angle and Segment Bisectors | To bisect something is to divide it into two congruent parts. So with that said, an angle or segment bisector is something that bisects an angle or segment. | As you can see angle (upper) and segment (right) bisectors run through the angle or segment and splits it into two congruent parts.

7: Real World Example: When an archer draws back and is about to fire, the string of the bow creates an obtuse angle and the arrow acts as the bisector of the angle.

8: Complimentary, Supplementary, and Vertical Angles | In the last chapter we reviewed angles and how they are measured in degrees. Depending on the two angles and the sum of the measures, the two angles could be classified as complimentary or supplementary angles. Two angles are complimentary if the sum of both of their measures equals 90 degrees. Two angles are supplementary if the sum of both of their measures equals 180 degrees. Two angles can also be vertical angles if they are not adjacent and their sides are formed by two intersecting lines. See the next page for real world examples. | These are vertical angles.

9: To the left is an example of complimentary angles. To the right is an example of supplementary angles. | Real World Example: The angles of the two sidewalks that are both angles that equal supplementary angles.

10: Chapter 3 Parallel Lines and Angles Formed by a Transversal | Parallel lines are two lines that are side by side and never intersect. Angles are formed when two parallel lines are cut (or intersected) by a transversal. Several pairs of congruent and supplementary angles are formed. | This is a transversal.

11: These are parallel lines. | Real World Example: The two yellow lines on the roads are parallel.

12: Perpendicular Lines | Perpendicular lines are formed when two lines meet and creates right angles. | This image depicts perpendicular lines.

13: Real World Example: The forty yard line meets the sideline and creates two right angles.

14: Chapter 4 Triangles | A triangle is defined as a plane figure with three straight sides and three angles. | These are each of the kinds of triangles. | Real World Example: When beginning a pool match the pool balls are set in the triangle to line them up for the break.

15: Angle Measurements Recap | Angles are measured in degrees. Angles are then classified according to their size. There are four different classifications depending on the measure of the angle's degrees. First there is the acute angle, an angle is classified acute if it is 0-89 degrees. Second is the right angle, an angle is classified as right if it is 90 degrees. Third is the obtuse angle, an angle is classified as obtuse when the angle measures to be 91-179 degrees. Finally an angle is also classified as a straight angle, an angle is classified as straight if it measures out to be 180 degrees. | These are the different angle measurements. | Real World Example: There are many different angles that are measured when measuring different triangles.

16: The Pythagorean Theorem and Distance Formula | In history there was a Greek philosopher named Pythagoras. Pythagoras is known for his discoveries in math and science. He is best known for his theorem, The Pythagorean Theorem. This theorem states that the sum of the areas of the two small squares equals the big one. Below is an image to show the theorem in algebraic terms. The distance formula is a variant of The Pythagorean Theorem. The distance formula is used to find the distance from one point to another on a coordinate grid. On the next page there will be an example concerning the formula. | This is an example of the Pythagorean Theorem.

17: This is how you solve a distance formula problem step by step. | Real World Example: Builders use The Pythagorean Theorem in order to know where to build certain things. | Real world Example: Teachers use the distance formula when teaching kids how to use the formula.

18: Chapter 5 Congruent Triangles | Two triangles are congruent when all corresponding sides and interior angles are congruent. There are five ways to tell if two triangles are congruent. These include SSS, SAS, ASA, AAS, and HL. | These are congruent triangles.

19: Real World Example: The pyramid sides needed to be congruent in order to look good.

20: Chapter 6 Polygons | Polygons are the classified as many-sided figures. A polygon's sides are all line segments. A polygon is named according to the number of sides that it has. Polygon's can only have line segments and no curves, if it has a curve then it is not a polygon. The least amount of sides that a polygon can possibly have is three. As long as the polygon has the correct amount of sides, then they can be any shape they want. | These are the first eight polygons and their names.

21: Real World Example: This house is labeled as a habitable polyhedron.

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  • Title: Geometry Scrapbook
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