Welcome To Geometry!

Overview of MT1: ConstructionsYour 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 edgeAbility to use a compassAbility to draw basic shapes, such as lines, triangles, squares, etc…Ability to memorize vocabulary wordsAbility to work independentlyAbility to use online resources for learning.

Overview of MT1: ConstructionsWhat will you turn in for your portfolio for GEO MT1?.

Twelve Definitions andFour 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: ConstructionsLet’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: ConstructionsLet’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: ConstructionsLet’s Start with Vocab:

Coplanar Def: Points on the same plane.

A, K, and J are coplanar

Parallellines

Def: Lines that are in the same plane but never intersect.

AB and CG are parallel (Symbol: I I )

Skewlines

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: ConstructionsLet’s Start with Vocab:

Perpendicular Lines

Def: Lines that cross and form 90o 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: ConstructionsNow 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: ConstructionsNow 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…

http://www.mathopenref.com/constructions.html

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.

Lines Angles Triangles

1. Copy a line segment2. Perpendicular bisector

of a line segment3. Parallel line through a

point

1. Bisecting an angle2. Copy an angle3. Construct a 30 degree

angle4. Construct a 45 degree

angle5. Construct a 90 degree

angle

1. Copy a triangle2. Isosceles Triangle, given

a base and side3. Equilateral Triangle4. Triangle Median