BC: Josh Morton Geometry 2nd Period December 4, 2012
FC: 90 Degrees to Learning By: Josh Morton November 17 2nd period
1: Table of Contents | Page 2 and 3: Conjecture, Line, and Intersection Pages 4 and 5: Angles, Sides, and Endpoints Page 6 and 7: Segment Bisector, Midpoints, and Bisect Page 8 and 9: Complementary, Supplementary, and Vertical Angles Page 10 and 11: Page 12 and 13: Perpendicular Lines Page 14 and 15: Triangles Page 16 and 17: Pythagorean Theorem and Distance Formula Page 18 and 19: Congruent Triangles Page 20 and 21: Polygons
2: A conjecture is an unproven statement that is based on a pattern or observation. | A line has one dimension. It extends without end in two directions. It is represented by one line with two arrowheads | 2.
3: The intersection of two or more figures is the point or points that the figures have in common | Real World Example: A telescope has a point, plane, and line. The line is to be considered the leg of the telescope. | 3.
4: 4. | An angle consists of two rays with the same endpoint. | An acute angle is an angle that's measure is between 0 and 90 degrees | An obtuse angle is an able with the measures between 90 and 180 degrees
5: Real world Example: The angle of a laptop. | 5. | A right angle is an angle with the measure of only 90 degrees | A straight angle is an angle that is only 180 degrees
6: A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. | The midpoint of a segment is the point on the segment that divides it into two congruent segments | To bisect a segment means to divide the segment into two congruent segments | 6.
7: Real World Example: When you cut a quarter of a cake into two congruent pieces, we are dividing along the angle bisector | 7.
8: If the two angles are complementary angles then the sum of their measures is 90 degrees. | If the two angles are supplementary angles then the sum of their measures is 180 degrees. | 8.
9: Two angles that are not adjacent and whose sides are formed by two intersecting lines are vertical angles | Real World Example: | 9.
10: Parallel lines are two lines that lie on the same plane and do not intersect. | Real World Example The double yellow lines on are road are parallel. | 10.
11: Alternate Interior Angles | Corresponding Angles Example | 11. | Alternate Exterior Angles | Same Side Interior Angles
12: Perpendicular Lines are two lines that intersect at a right angle | A cross is the perfect real world example of perpendicular lines. | 12.
13: The letter "T" is another perfect real world example of perpendicular lines. | 13.
14: A triangle is a figure formed by three segments joining three non collinear points, called verticies. | Real world example | 14. | Isosceles Triangle at least two congruent sides | Equilateral Triangle has three congruent sides | Scalene triangle has no congruent sides
15: Obtuse triangle is a triangle wit one obtuse angle | 15. | Acute triangle is a triangle with one acute angle | Right triangle is a triangle with one right 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. | A2 + B2 = C2 | 16.
17: Distance Formula: If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is ((x2-x1)2 + (y2-y1)2 )2 | Real World Example of the Pythagorean Theorem
18: Congruent triangles are triangles that have the same size and the same shape | The five ways to prove that a triangle is congruent are, Angle Side Angle, Angle Angle Side, Hypotenuse Leg, Side Angle Side, and Side Side Side | 18.
19: Angle Side Angle | Angle Angle Side | Side Side Side | Hypotenuse Leg | Side Angle Side | 19.
20: A polygon is a plane figure that is formed by three or more segments called sides. Each side intersect exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon. | A rhombus is a parallelogram with four congruent sides. | 20. | A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
21: A rectangle is a parallelogram with four right angles | A square is a parallelogram that has four right angles and congruent side. | A stop sing is a polygon. A stop sign is known as an octagon. | 21.