points, lines, and planes 1.2 ms. verdino. what will we be learning today? spi 3108.1.4: use...

15
Points, Lines, and Planes 1.2 Ms. Verdino

Upload: sophia-gilbert

Post on 02-Jan-2016

213 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Points, Lines, and Planes1.2Ms. Verdino

Page 2: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

What will we be learning today?

SPI 3108.1.4: Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.

Objective

To understand basic terms and postulates of geometry.

Page 3: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Euclid300 BC

• Born in Greece• Wrote the book the “Elements”• Known as the Father of geometry• Developed 5 postulates• 3 undefined definitions

Page 4: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

The undefined terms• Point: Indicates a location and has no size.

• Line: Represented by a straight path that extends in two oppositedirections without end and has no thickness. A line also contains infinitely many points.

• Plane: Represented by a flat surface that extends without end and has no thickness. A plan contains infinitely many lines.

Page 5: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

• Collinear points: Points on the same line.

• Coplanar points: Points and lines that lie in the same plane.

1. What are two other ways to rename CE ?

2. What are two other ways to rename plane X ?

3. What are the names of three collinear points? What are the names of four coplanar points?

Page 6: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Your turn!

1. What are two other ways to name plane V?

2. Name three collinear points.

3. Are points R, N, M, and X coplanar?

4. Name four coplanar points.

Page 7: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

• Space: The set of all points in three dimensions.

• Segment: Part of a line that consists of two endpoints and all points between them.

• Ray: Part of a line that consists of one endpoint and all the points of The line on one side of the endpoints.

• Opposite rays: Two rays that share the same endpoint and form a line.

Page 8: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

1. Name four segments on the figure above.

2. Name four rays on the figure above.

3. Name 2 pairs of opposite rays on the figure above.

Page 9: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Your turn!

1. What are the names of the segments in the figure above?

2. What are the names of the rays in the figure above?

3. Which of the rays in part 2 are opposite rays?

Page 10: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Postulates and Axioms

• Postulate/Axiom : An accepted statement of fact. : Building blocks of the logical system in geometry.

• Theorem: A general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths

Through any two points there is exactly one line.

Postulate 1-1

Page 11: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Postulate 1-2

When you have two or more geometric figures, the intersection is the set of points that figures have in common.

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

Page 12: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Postulate 1-3

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

Page 13: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Postulate 1-4

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

Page 14: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Each surface in the figure on the rightrepresents a plane. What is the intersection of plane ADC and plane DRQ?

What plane contains points B, C, and Q?

Page 15: Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI 3108.1.4: Use definitions, basic postulates, and theorems about points,

Your turn!

What is the intersection of plane ABC and EFB?

What plane contains points E, F, and C?