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Aim: What is Geometry? Do Now: Write an algebraic expression for each of this phrases: 3 more than w r decreased by 2 the product of 5r and s twice x decreased by 10 Aim: What is Geometry Course: Appl. Geo. geo metreinFrom the Greek - “To measure the earth.” Aim: What is Geometry Course: Appl. Geo. Geometry Basics Undefined Terms Point - Location, it has no dimension •P Straight Line C A - Collection of points; extends indefinitely in both directions D B AB - symbolically Collinear – Points that lie on same line - A, B, C, D are collinear. Plane A B •x D P •y C - A set of points suggested by a flat surface P or ABCD Aim: What is Geometry Course: Appl. Geo. Coplanar – Points and/or lines that lie on same plane - points x and y are coplanar Geometry Basics Line Segment A B - Part of a line; between two points on a line AB Midpoint M E EM MF Ray F - A point on a line segment that is equidistant from the endpoints of the line segment - A part of a line that has one G H endpoint and extends GH indefinitely in the other - congruent direction Course: Appl. Geo. exactly sameAim: What is Geometry size and shape Refer to diagram below in answering: E C G S R P O D B A F H 1. Which lines intersect at Point R? CD & GH 2. Name 3 rays with endpoint S. SD SC SE 3. Name 3 line segments on AB. AP PO PB 4. Which line intersects EF? Aim: What is Geometry CD Course: Appl. Geo. M is the midpoint of AB A 12 M B 3x + 3 1. If AB measure 8”, find the length of AM of MB 4” 4” 2. If AM measures 10 feet, find the length of AB of MB 20’ 10’ 3. If AM = 12 and MB = 3x + 3, find the value of x 12 = 3x + 3 9 = 3x 3 =x Aim: What is Geometry Course: Appl. Geo. Model Problem A M B 2x + 18 The length of AB is 2 x 18. How long is it from A to M , the midpoint of AB? Aim: What is Geometry Course: Appl. Geo. Aim: What’s your angle? Do Now: Use sketchpad to draw and measure angles Aim: What is Geometry Course: Appl. Geo. B O A Vertex Angle - Two rays that have the same endpoint, called a vertex To identify an angle use the symbol and letters of the rays. The vertex letter is in the middle. Ex. AOB or BOA Aim: What is Geometry Course: Appl. Geo. What’s in a name? C B D E O What’s another name for A AOC? BOC? DOA? COD? Aim: What is Geometry Course: Appl. Geo. B protractor O A Vertex A common standard measure of an angle is the degree - 1/360 of a circle, written as 10. A protractor is a tool used for measuring the number of degrees in an angle. Aim: What is Geometry Course: Appl. Geo. Angle Types C B D E O Right Angle measures 900 A AOC Acute Angle - angle less than 900 AOB is an acute angle Straight Angle - 1800 AOE Obtuse Angle - less than 1800 but AOD greater than 900 Aim: What is Geometry Course: Appl. Geo. Sketchpad With Sketchpad 1) Draw and label and measure a) an acute angle b) a straight angle c) a right angle d) an obtuse angle 2) Next to each, use the Text tool to type a definition of each. Example: ‘an acute angle is an angle that measures . . . . (you fill in the rest)’ 3) Type your name at the bottom of the sketch and save to flash drive. Aim: What is Geometry Course: Appl. Geo. What’s my name? C B D E O A Name two right angles Name as many acute angles as possible Name 2 obtuse angles Name a straight angle Aim: What is Geometry Course: Appl. Geo. Model Problems Determine the type of angle and then estimate the measure of each. A C B C D Angles that are equal in measure are congruent Aim: What is Geometry Course: Appl. Geo. D Angle Types C B D E O A Adjacent Angles - Two angles that have the same vertex and share a common side AOB & BOC BOC & COD COD & DOE Linear Pair - Two angles that are adjacent and supplementary ex. AOB & BOE Aim: What is Geometry Course: Appl. Geo. Addition Postulate C B D E O A AOB + BOC = AOC If mAOB is 37o and mBOC is 53o, what is the measure of AOC? If mBOC is 33o and mCOD is 63o, what is the measure of BOD? Aim: What is Geometry Course: Appl. Geo. Model Problems Q P V N M If mMQV = 90 and mVQP is 35, what is mMQP? If mMVQ = 55, what is mQVP? Judging by appearances, name a) two acute angles b) two obtuse angles c) two right angles Aim: What is Geometry Course: Appl. Geo. Model Problems Q P V M N MVP is a straight angle. If mMVQ is xo and mQVP is 2xo, what is value of x? If mMNP = 165 and mMNQ = 2x – 3 and mQNP = 2x + 7, what is value of x? Aim: What is Geometry Course: Appl. Geo.