Warm Up1) Write the Distance Formula

22 )()( 1212 yyxxd

2,

22121 yyxx

2) Write the Midpoint Formula

3) Three segment measures are given. The three points named are collinear. Determine which point is between the other two.

AB = 12, BC = 5, AC = 17

Line Segment Review Three segment measures are given. The three points named are collinear. Determine which point is between the other two.

AB = 12, BC = 5, AC = 17

A C

17”

B

12” 5”

B CA

12” 17” 5”

What are the steps to find the point between the other two points?

Line Segment Review Three segment measures are given. The three points named are collinear. Determine which point is between the other two.

AB = 12, BC = 5, AC = 17

B CA

12” 17” 5”

Segment Addition PostulationIf 3 points A, B, and C are collinear and B is

between A and C, then AB + BC = AC

“Segments and Properties of Real Numbers” worksheet #1-6 and “Distance and Midpoints” due on Friday, 8/27

Warm Up1) C is the midpoint of segment AB. Find AC, CB, and AB.

2) Find x if segments 66, xABCDAB , and CD = 24

CAB

12 x 43 x

Warm Up1) C is the midpoint of segment AB. Find AC, CB, and AB.

CAB

12 x 43 x

AC = CB2x + 1 = 3x – 4

2x + 5 = 3x5 = x

AC = 2x + 1 = 2(5) + 1 = 11CB = 3(5) – 4 =11

AC and CB are both 11, which is half of 22, the length of segment AB.

Warm Up

2) Find x if segments 66, xABCDAB , and CD = 24

AB = CD6x – 6 = 24

6x – 6 + 6 = 24 +66x = 30X = 5

Review of Points, Lines, Planes, and Angles

Prepared by Ms. Ngo8/21/10

A

D

P

C B

F5 cm G

5 cm

Review of Points, Lines, Planes, and Angles

A

D

P

C B

F 2) What lines do they intersect the plane P? 

CBCDBD ,,

1) Name the lines that lie on the plane P. 

ACABAE ,,

E3) Name five triple non-collinear points

Points C, F, and D; points C, B, and D; Points A, C, and D; points A, B, and D, etc.

5 cm

5 cm

G

A

D

P

C B

F5) List three segments that lie on the plane P. 

4) Are the plane P and the plane P that is determined by the three points B, C, and D the same?  

CBDBCD ,,

E6) Draw the ray AE by using the pen or highlighter.

Yes, points B, C, and D are co-planar. Postulate states that 3 different collinear points determine a plane. D

7) How do you represent the length of the following segments CBDBCD ,,CBDBCD ,,

5 cm

5 cm

G

A

D

P

C B

F

9) Besides the plane P, can you list other planes? 

8) What is the length of the segment

E11) What is the intersection line between the plane P and plane ACD?

CD = 3 cm

5 cm

CD

Plane ACD, plane ABD, plane ACB, plane CFD, plane CDB, etc.

10) Are the plane ADB and the plane ABE the same? Explain.

Does point E lies on the plane ABD? Yes, because it lies on the line . The line lies on the plane ABD so point E lies on the plane ABD.

AD AD CD

5 cm

G

A

D

P

C B

F

13) How many points are there in a given plane? 

12) Is ADE a plane? Explain your reason.

E

16) Between a given plane and a line, which one has more points than the other?

No, these points are collinear.

5 cm

INFINITE

14) How many points are there on a line?

INFINITE

15) How many points are there on a segment ?AB

INFINITE

A plane has more points than a line. Also, the line is one-dimension. The plane is two-dimension.

5 cm

G

A

D

P

C B

F

18) How do you represent segment CD congruent to AC? 

17) Does a plane lie on a line?

E

No; a plane contains infinite lines. 5 cm

ACCD 5 cm G

18) What point is the midpoint of ? BD

G is the midpoint of segment BD.

Conclusion

• What are two things that you think are important from today’s lesson?

• What is one question that you still have

about the information from today’s lesson? Where is it in the lesson?