Good to see you

To warm up today, please get: ♥ a piece of isometric dot paper ♥ Straight edge ♥ the slip of paper from the back desk ♥ Please create the 3 drawings.

1.2

Building Blocks of Geometry

Basic Geometric Figures

Undefined terms: ♥ Line ♥ Point ♥ Plane

Point

• Points are often shown as dots, you may even think of them as stars in the night sky.

HOW TO WRITE: ♥ Points are named as ONE capital letter P • A • • M T • X • P m Q M, T, A

Lines

• A line has no thickness, is perfectly straight, and has infinite length.

HOW TO WRITE: ♥ Lines are named by any two points (capital letters) on the line, with a double-headed arrow over the two letters.

• A • • M T • X • P m MT, PM Q Or ♥ a single lowercase script letter.

m

Plane

• A plane extends infinitely in all directions along a flat surface.

HOW TO WRITE: ♥ A plane can be named by three non-collinear points (THREE capital letters) that lie in the plane.

MXA Or ♥ It can be named by one script capital letter.

Q • A • • M T • X • P m Q

Collinear

♥ Points on the same line M, X, P are collinear.

M, X, A are non-collinear • A • • M T • X • P m Q

Coplanar

♥ Points on the same plane M, X, A are coplanar

Segment

• A segment is a part of a line that begins at one point and ends at another. The points are called the endpoints of the segment.

♥ HOW TO WRITE: – The endpoints are capital letters and have a bar over them.

• A • • M T • X • P m Q __ __ XP, TX

Ray

♥ A ray is a part of a line that starts at a point and goes forever in one direction. ♥ The point is called the endpoint of the ray ♥ HOW TO WRITE: Two capital letters with a ray on top. Be sure to have the endpoint above the endpoint letter!

• A • • M T • X • P m Q XP, PM

Angle

A ♥ An angle is formed by two rays with a common endpoint. (DEFINITION) B ♥ The common endpoint is called the vertex of the angle and the rays are the sides of the angle.

Exterior

♥ An angle divides a plane into two regions: the interior and the exterior .

vertex side side Interior C ♥ HOW TO NAME IT: Use THREE capital letters with the vertex in the middle and the angle sign in front. The three letters need to be in the order that they would be if you traced the angle with your finger.

OR By the angle sign and the vertex ONLY IF there is only one angle at the vertex.

Postulate

A postulate is a statement that is accepted as true without proof.

In other words, a postulate is so obvious, and makes so much sense, there is no need to prove it.

Our first 4 postulates

1. Through any two points there is exactly one line.

2. If two distinct lines intersect, then they intersect in exactly one point.

3. If two distinct planes intersect, then they intersect in exactly one line.

4. Through any three noncollinear points there is exactly one plane.

Your assignment

♥ 1.2 R & P