Welcome To Geometry!

Overview of MT1: Constructions Your first MT in Geo is going to teach you some vocabulary and show you the process for drawing different shapes, lines, and angles. Skills you should already have… Ability to use a ruler or straight edge Ability to use a compass Ability to draw basic shapes, such as lines, triangles, squares, etc… Ability to memorize vocabulary words Ability to work independently Ability to use online resources for learning.

Overview of MT1: Constructions What will you turn in for your portfolio for GEO MT1?. Twelve Definitions and Four Postulates with a Passed quiz for evidence Twelve Constructions with a description of the process on 5 of them. A quiz on five of the constructions randomly chosen. Staple and turn in to your LF

Overview of MT1: Constructions Let’s Start with Vocab: Point Def: A point in space. Use any capital letter in the Alphabet. Point C, M, and Q Line Segment Def: Part of a line made of two ending points. CD is a line segment. Line Def: A series of points that go on in both directions AB is a line segment.

Overview of MT1: Constructions Let’s Start with Vocab: Ray Def: A part of a line that has an endpoint and goes on in the other direction. AB is a Ray Colinear Def: Points on the same line. A and N are Collinear. Plane Def: A flat surface with no thickness. It take at least 3 non-collinear points to make a plane. Plane BCG or Plane ABG, etc… T and I are Collinear.

Overview of MT1: Constructions Let’s Start with Vocab: Coplanar Def: Points on the same plane. A, K, and J are coplanar Parallel lines Def: Lines that are in the same plane but never intersect. AB and CG are parallel (Symbol: I I ) Skew lines Def: Lines that are not on the same plane, not parallel, and do not intersect CB and DE are skew lines. A, B, D are not coplanar

Overview of MT1: Constructions Let’s Start with Vocab: Perpendicular Lines Def: Lines that cross and form 90 o angles. BA and AF are perpendicular. Congruent Def: Objects that are the same size and same shape. BAFH and CGED are congruent (Symbol: ≅ ) Postulate Def: An accepted statement of fact.

Overview of MT1: Constructions Now some postulates: Postulate 1.1: Through any two points, there is exactly one line. Only 1 line through A and B Postulate 1.2: If two lines intersect, then they intersect at exactly one point. AE and BD intersect at C Postulate 1.3: If two planes intersect, then they intersect at exactly one line. Plane R and Plane W intersect at line ST

Overview of MT1: Constructions Now some postulates: Postulate 1.4: Through any three non-collinear points, there is exactly one plane. Only 1 line through A and B

You are now going to need access to a compass and straight edge (ruler). The table shows the list of 12 constructions you are going to have to master. The process for constructing each of these shapes can be found at the website… Make sure your name and period are at the top of each page. Each construction should have the title listed above your drawing. DO NOT try to crowd the drawing on one page. At the most, you may put two drawings per page. Furthermore, you must describe in detailed paragraph format the steps for your constructions for FIVE of the TWELVE drawings (your choice). When done, your LF will ask you to construct five of the drawings without error as proof of your learning. LinesAnglesTriangles 1.Copy a line segment 2.Perpendicular bisector of a line segment 3.Parallel line through a point 1.Bisecting an angle 2.Copy an angle 3.Construct a 30 degree angle 4.Construct a 45 degree angle 5.Construct a 90 degree angle 1.Copy a triangle 2.Isosceles Triangle, given a base and side 3.Equilateral Triangle 4.Triangle Median