Lesson 1.1Building Blocks of Geometry

Good Morning

Geometry - Lesson 1.1/ 1-31 oddsQuiz Friday – Lesson 1.1

Homework:

Basic Geometric Figures

• Undefined terms:♥Line♥Point♥Plane

Point

• Points have NO size and are often shown as dots.

HOW TO WRITE:

♥ Points are named as ONE capital letter such as A or X

.A

Lines• A line has no thickness, but has infinite

length. It is an straight arrangement of an infinite amount of points.

HOW TO WRITE: ♥ Lines are named by two points (capital

letters) on the line, topped with miniature version of a line on top.

Or♥ a single lowercase script letter. m

Y. X.

line m

Plane• A plane has length and width, but no height. It

extends infinitely in all directions along a flat surface.

HOW TO WRITE:♥ A plane can be named by three points

(THREE capital letters) that lie in the plane.

Or

♥ It can be named by one script capital letter

such as R.

C.B.

A. Plane ABC

RPlane R

Collinear♥ Points on the same line, together.

Coplanar♥ Points, lines, …, on the same plane,

together

C.B.

A.

Y. X.Z.Points X, Y, & Z are collinear

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.

G H

Ray♥ A ray is a part of a line that starts at a

point and goes infinitely 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!

P Q

Q P

Angle♥ An angle is formed by two rays with a common endpoint.

♥ The endpoint is called the vertex of the angle and the rays are the sides of the angle.

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

Angles♥ 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.

ORBy the angle sign and the vertex ONLY IF

there is only one angle at the vertex.

D

E

F

Multiple angles with a shared vertex

D E

B CA

There are 4 angles with vertex B, therefore each angle MUST be named using 3 points

specific to that angle.

Midpoint

• Midpoint of a segment is the point on the segment that is the same distance from both endpoints– bisects the segment– divides the segment into two congruent segments

• Congruent markings on a segment indicate a point is a midpoint

●●●

Congruent markings, aka, slash marks

QU E

Midpoint of WHAT?• Can a point have a midpoint ?

– a line?– a square?– a plane?

– NO, only a segment is finite in length– There is NO midpoint to infinity

Conjectures

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

In other words, a conjecture is so obvious, and makes so much

sense, there is no need to prove it.

1. The intersection of two lines is a ________

2. The intersection of two planes is a ______.

3. Through any two points there is exactly one _______.

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

5. If two points are in a plane, then the line containing them ____________________.

Our first 5 ConjecturesPOINT

LINE

LINE

PLANE

IS ALSO IN THE PLANE.