holt mcdougal geometry 1-1 understanding points, lines, and planes 1-1 understanding points, lines,...

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes1-1 Understanding Points, Lines, and Planes

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Holt McDougal Geometry

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Identify, name, and draw points, lines, segments, rays, and planes.

Apply basic facts about points, lines, and planes.

Objectives

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

undefined term pointline planecollinear coplanarsegment endpointray opposite rays

postulate

Vocabulary

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Points that lie on the same line are collinear. K, L, and M are collinear. K, L, and N are noncollinear. Points that lie on the same plane are coplanar. Otherwise they are noncoplanar.

M

K

L

N

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Example 1: Naming Points, Lines, and Planes

A. Name four coplanar points.

B. Name three lines.

A, B, C, D

Possible answer: AE, BE, CE

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Use the diagram to name two planes.

Check It Out! Example 1

Possible answer:

Plane R and plane ABC.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

SOLUTION

EXAMPLE 1

Name points, lines, and

planes

b. Name three points that are collinear.

Name four points that are coplanar.

Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.

a. Give two other names for PQ and for plane R.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesEXAMPLE 1

Name points, lines, and planes

b. Points S, P, and T lie on the same line, so they are collinear.

c. Points S, P, T,and V lie in the same plane, so they are coplanar.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesGUIDED PRACTICE for Example

1

ANSWER TS, PT; point V

1. Use the diagram in Example 1. Give two other names for ST . Name a

point that is not coplanar with points Q, S, and T.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesExample 2: Drawing Segments and Rays

Draw and label each of the following.

A. a segment with endpoints M and N.

B. opposite rays with a common endpoint T.

MN

T

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Draw and label a ray with endpoint M that contains N.

Check It Out! Example 2

M N

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Name a line that passes through two points.

Example 3: Identifying Points and Lines in a Plane

XY

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Name a plane that contains three noncollinear points.

Check It Out! Example 3

Possible answer: plane GHF

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesExample 4: Representing Intersections

A. Sketch two lines intersecting in exactly one point.

B. Sketch a figure that shows a line that lies in a plane.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Check It Out! Example 4

Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesEXAMPLE 3Sketch intersections of lines and planes

a. Sketch a plane and a line that is in the plane.

b. Sketch a plane and a line that does not intersect the plane.

c. Sketch a plane and a line that intersects the plane at a point.

SOLUTIONa. b. c.

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesEXAMPLE 4

Sketch intersections of planesSketch two planes that intersect in a line.

SOLUTION

Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed

lines to show where one plane is hidden.

STEP 2

Draw: the line of intersection.STEP 3

Draw: a vertical plane. Shade the plane.

STEP 1

Holt McDougal Geometry

1-1 Understanding Points, Lines, and PlanesGUIDED PRACTICE for Examples

3 and 44. Sketch two different lines that intersect a plane at the same point.

Use the diagram at the right.

5. Name the intersection of PQ and line k.

ANSWER Point M

ANSWER

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Lesson Quiz: Part I

1. Two opposite rays.

3. The intersection of plane N and plane T.

4. A plane containing E, D, and B.

2. A point on BC.

CB and CD

Possible answer: D

Possible answer: BD

Plane T

Holt McDougal Geometry

1-1 Understanding Points, Lines, and Planes

Lesson Quiz: Part II

5. a line intersecting a plane at one point

6. a ray with endpoint P that passes through Q

Draw each of the following.