Objectives: To use inductive reasoning to make conjectures

 Inductive Reasoning  reasoning that is based on observed patterns. If you see a pattern or sequence, you can use inductive reasoning to tell what the next term in the sequence will be.  Conjecture:  a conclusion reached by using inductive reasoning.

 Ex: Use inductive reasoning to find the next two terms in each sequence. 3, 6, 12, 24 …A, B, C, D … Mon, Tue, Wed …O, T, T, F, F, S, S …

 Not all conjectures turn out to be true. You can prove that a conjecture is false by finding one counterexample.  Counterexample  an example for which the conjecture is incorrect/false.

 Ex: Find a counterexample for each conjecture. The square of any number is greater than the original number. You can connect any three points to form a triangle. Any number and its absolute value are opposites.

 Homework Formatting ◦ All homework must be done in pencil. Homework done in pen will not be accepted. ◦ Write and circle the problem number. ◦ Box your answer. ◦ Attempt every problem even if you are unsure. I will go over homework questions the next day so make sure you ask if you have a question. This is important because many quiz and test questions will come directly from the homework.

 Homework #1  Due Tuesday (Aug 14)  Page 6 – 7  # 2 – 18 even  #25 – 28 all

 Objectives: To understand basic terms of geometry To understand basic postulates of geometry

 Point  think of as a location. It has no size. It is represented by a small dot and is named by a capital letter.  Space  the set of all points.  Line  a series of points that extends in two opposite directions without end. You can name a line by any two points on the line or with a single lowercase letter.  Collinear points  points that lie on the same line.

Name each line. Are points E, F, and C collinear? Are points E, F, and D collinear? Are points F, P, and C collinear? E F C D P n m r

 Plane  a flat surface that has no thickness. A plane contains many lines and extends without end in the directions of all its lines. ◦ Planes are named by either a single capital letter or by at least three of on its non-collinear points.  Coplanar  points and lines that lie in the same plane.

 Postulate/Axiom  an accepted statement of fact.  Postulate 1.1 ◦ Through any two points there is exactly one line.  Postulate 1.2 ◦ If two lines intersect, then they intersect in exactly one point.

 Postulate 1.3 ◦ If two planes intersect, then they intersect in exactly one line.  Postulate 1.4 ◦ Through any three non-collinear points there is exactly one plane.

 Homework #2  Due Wednesday (Aug 15)  Page 19 – 20 ◦ # 1 – 33 odd

 Objectives: To identify segments and rays To recognize parallel lines

 Segment  the part of a line consisting of two endpoints and all points between them. AB endpoint Segment AB AB

 Ray  the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint. XY endpoint Ray YX YX

 Opposite Rays  two collinear rays with the same endpoint. Opposite rays always form a line. QR S RQ and RS are opposite rays Shared endpoint

 Ex: Name all the segments and rays in the figure below. Are there any opposite rays? L P Q

 Parallel Lines  coplanar lines that do not intersect.  Skew Lines  are non-coplanar; therefore, they are not parallel and do not intersect.  Parallel Planes  planes that do not intersect. Lines and planes can also be parallel as long as they do not intersect.

 Ex: Identify any parallel lines, parallel planes, and skew lines in the figure below. A B C D E F G H

 Homework #3  Due Thursday (Aug 16)  Page 25 – 26 ◦ #1- 33 odd  Quiz Friday (1.1 – 1.5)

 Objectives: To find the lengths of segments

 Postulate 1.5 – Ruler Postulate ◦ The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. AB a b

 Congruent (=) Segments  segments with the same length. For example, if AB = 2cm and CD = 2cm then we can say: AB = CD ~ ~

 Postulate 1.6 – Segment Addition Postulate ◦ If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C AB + BC = AC

 Ex: EG = 100. Find the value of x. Then find EF and FG. EFG 4x - 202x + 30

 Midpoint  a point that divides the segment into two congruent segments. A midpoint, or any line, ray, or other segment through a midpoint, is said to bisect the segment.

 Ex: C is the midpoint of AB. Find AC, CB, and AB. ACB 2x + 13x - 4

 Homework #4  Due Friday (Aug 17)  Page 33 – 34 ◦ # 1 – 19 odd  Quiz Tomorrow

 Objectives: To find the measures of angles To identify special angle pairs

 Angle  formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. T B Q 2 vertex Can be named: <TBQ, <QBT, <B, or <2

 Angles can be classified by their measure x° Acute Angle 0 < x < 90 x° Right Angle X = 90 x° Obtuse Angle 90 < x < 180 x° Straight Angle X = 180

 Congruent Angles  angles with the same measure.  Postulate 1.8 – Angle Addition Postulate ◦ If point B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC. ◦ If <AOC is a straight angle, then m<AOB + m<BOC = 180 A O B C

 Some angle pairs have special names.  Vertical Angles  two angles whose sides are opposite rays.  Adjacent Angles  two coplanar angles with a common side, a common vertex, and no common interior points.  Complementary Angles  two angles whose measures have a sum of 90°  Supplementary Angles  two angles whose measures have a sum of 180°

 Homework # 5  Due Tuesday (Aug 21)  Page 40 ◦ # 1 – 23 all

 Objectives: To find the distance between two points in the coordinate plane. To find the coordinates of the midpoint of a segment in the coordinate plane.

Origin (0,0) Quadrant I (+,+) Quadrant II (-,+) Quadrant III (-,-) Quadrant IV (+,-)

 Ex: Find the distance. T(5, 2) and R(-4, -1) A(1, -3) and B(-4, 4)  Find the midpoint. Q(3, 5) and R(7, -9) X(2, -5) and Y(6, 13)

 Homework # 6  Due Wednesday (Aug 22)  Page 56 ◦ # 1 – 31 odd

 Objectives: To find perimeters of rectangles and squares, and circumferences of circles. To find areas of rectangles, squares, and circles.

s s

Rectangle  Perimeter = b + b + h + h -or- P = 2b + 2h  Area = b · h -or- A = bh b b hh

d r

 Ex: Find the perimeter and area of a square with side lengths 8cm. Find the perimeter and area of a rectangle with base 4m and height 8m. Find the circumference and area of a circle with diameter 10mm.

 Postulate 1.9 ◦ If two figures are congruent, then their areas are equal.  Postulate 1.10 ◦ The area of a region is the sum of the areas of its non-overlapping parts.

 Homework #7  Due Thursday (Aug 23)  Page 65 ◦ # 1 – 31 odd