BC: The End
FC: Discovering the fun of Geometry! Tsz Yan Lee Period5 | Geometry Scrapbook
1: Table of Contents | 1 | Midpoints --------------------P.2-3 Polygons----------------------P.4-9 Disjunctions and Conjunctions-------P.10-11 Angle Relationships-------------P.12-15 The Properties of Isoceles Triangle-P.16-17 Isosceles and Equilateral Triangles-P.18-19 Identifying Quadrilaterals-----------P.20-21 Inductive Reasoning--------------P.22-23 Inverse, Converse, and Contrapositives-P.24-26 Geometry Jokes-------------------------P.27 The Triangle Sum Conjecture-------P.28-29 The Polygon Sum Conjecture--------P.30-32
2: Midpoint | A midpoint is the point on a line segment that is the same distance from both endpoints.
3: The midpoint, (1+4)/2 , (1+3)/2 = (2.5, 2)
4: Polygons | Polygons: A closed figure formed by joining three or more line segments in a plane at their endpoints with each line segment joining exactly two others. | Side of a polygon: Each line segment that forms a polygon. | Vertex of a polygon: Each point where two sides of a polygon meet. The plural of vertex is vertices.
5: Diagonal: A line segment that joins two nonconsecutive vertices of a polygon. | Regular polygon: A polygon in which all sides have the same length and all angles have the same measure.
7: Equilateral Polygon: When all sides have equal lengths | Equiangular Polygon: When all angles have equal measures
8: Convex Polygon: A polygon whose each of the interior angle measures less than 180
9: Concave Polygon: If one or more than one angle in a polygon measures more than 180 then it is known as concave polygon.
10: Disjunctions and Conjunctions | Disjunctions: A compound statement formed by joining two or more simple statements with the word OR | Disjunctions: Truth Table
11: Conjunctions: A compound statement formed by joining two or more simple statement with the word "AND" | Conjunctions: Truth Table
12: Angle Relationships | Acute angle: An angle with measure greater than 0 and less than 90 degrees. | Obtuse Angle: An angle with measure greater than 90 and less than 180 degrees.
13: Right angle: An angle with measure equal to 90 degrees. | Straight angle: An angle with measure 180 degrees. | Complementary angle: Two angles for which the sum of their measures is 90 degrees.
14: Supplementary Angles: Two angle for which the sum of their measures is 180 degrees. | Adjacent Angles: Two angles that share a common side but do not overlap each other.
15: Vertical Angles: When two lines intersect, the angles are always equal in measure and called vertical angles.
16: The Properties of Isosceles Triangle | If a triangle is isosceles, then its base angles are congruent. | The Isosceles Triangle Conjecture
17: Converse of the Isosceles Triangle Conjecture | If a triangle has two congruent triangles, then it is an isosceles triangle.
18: Isosceles and Equilateral Triangles | Vertex Angle Bisector Conjecture | In an isosceles triangle, the bisector of the vertex angle is also the altitude and the median to the base.
19: Equilateral/ Equiangular Triangle Conjecture | Every equilateral triangle is equiangular, and, conversely, every equiangular triangle is equilateral.
20: Identifying Quadrilaterals | Trapezoid: A quadrilateral having two parallel sides. | Kite: is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. | Parallelogram: is a simple (non self-intersecting) quadrilateral with two pairs of parallel sides
21: Rhombus: is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. | Rectangle: is any quadrilateral with four right angles
22: Inductive Reasoning | Inductive Reasoning is a type of reasoning that allows you to make conclusions based on a pattern of specific examples or past events. It is the process of observing data, recognizing patterns and making generalizations about those patterns.
23: Example: | Answer: D
24: Inverse, Converse and Contrapositive | Inverse: The inverse of a conditional statement is formed by negating (inserting "not") the hypothesis and the conclusion. | Conditional: If I am sleeping, then I am breathing. | Inverse: If I am not sleeping, then I am not breathing. | P Q | The inverse of | is | ~P ~Q
25: Converse: The converse of a conditional statement is formed by switching the hypothesis and the conclusion. | The converse of | P Q | is | Q P | Conditional: If I am sleeping, then I am breathing. | Converse: If I am breathing, then I am sleeping.
26: Contrapositive: The contrapositive if a conditional statement is formed by negating and switching the hypothesis and conclusion. | The contrapositive of | P Q | ~Q ~P | is | Conditional: If I am sleeping, then I am breathing. | Contrapositive: If I am not breathing, then I am not sleeping.
27: Geometry Jokes | Q: Why did the obtuse angle go to the beach? A: Because it was over 90 degrees. | Q. What shape is usually waiting for you at Stabucks? A. A line.
28: The Triangle Sum Conjecture | Triangle Sum Conjecture: The sum of the measures of every triangle is 180 degrees.
29: Triangle Exterior Angle Conjecture: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. | C+D=A
30: The Polygon Sum Conjecture | Quadrilateral Sum Conjecture: The sum of the measures of the four angles of any quadrilateral is 360 degrees
31: Pentagon Sum Conjecture: The sum of the measures of the five angles of any pentagon is 540 degrees | a+b+c+d+e=540
32: Polygon Sum Conjecture: The sum of the measures of the n interior angles of an n-gon is 180(n-2) degrees
33: The End