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Lesson 1-2 Warm-Up


Name three collinear points.

What is another name for AB?

Name a line in plane Z.
                                                     A.    A
Name the intersection of planes Z and W.             B.    B
How many lines are in plane Z?
                                                     C.    C
                                       0%   0%   0%  D.
                                                      0%   D


                                      A




                                            B




                                                 C




                                                      D
Over Lesson 1–1


Name three collinear points.

A. A, B, Q


B. B, Q, T
                                              A.    A
C. A, B, T                                    B.    B
                                              C.    C
D. T, A, Q
                                     0%   0%  D.
                                               0%   D
                                                    0%




                                     A




                                          B




                                               C




                                                    D
Over Lesson 1–1


What is another name for AB?

A. AA


B. AT
                                             A.    A
C. BQ                                        B.    B
                                             C.    C
D. QB
                                    0%   0%  D.
                                              0%   D
                                                   0%




                                    A




                                         B




                                              C




                                                   D
Over Lesson 1–1


Name a line in plane Z.

A. AT


B. AW
                                               A.    A
C. AQ                                          B.    B
                                               C.    C
D. BQ
                                      0%   0%  D.
                                                0%   D
                                                     0%




                                      A




                                           B




                                                C




                                                     D
Over Lesson 1–1


Name the intersection of planes
Z and W.

A. BZ


B. AW                                         A.    A
                                              B.    B
C. AB
                                              C.    C
D. BQ                                0%   0%  D.
                                               0%   D
                                                    0%




                                     A




                                          B




                                               C




                                                    D
Over Lesson 1–1


How many lines are in plane Z?

A. 2


B. 4
                                                A.    A
C. 6                                            B.    B
                                                C.    C
D. infinitely many
                                       0%   0%  D.
                                                 0%   D
                                                      0%




                                       A




                                            B




                                                 C




                                                      D
Over Lesson 1–1


Which of the following statements is always false?

A. The intersection of a line and
   a plane is a point.
B. There is only one plane
   perpendicular to a given                    A.   A
   plane.
C. Collinear points are also
                                               B.   B
   coplanar.                                   C.   C
D. A plane contains an infinite      0%   0%
                                               D.
                                               0%
                                                    D
                                                    0%
   number of points.
                                     A




                                          B




                                               C




                                                    D
• line segment
• betweenness of points
• between
• congruent segments
• construction
You identified and modeled points, lines, and
planes. (Lesson 1–1)




• Measure segments.
• Calculate with measures.
A line segment consists of two endpoints and all points
between the endpoints.




A segment with endpoints A and B can be named
AB or BA.

The length or measure of a segment always includes a unit
of measure such as meter or inch.
Length in Metric Units

A. Find the length of AB using the ruler.




The ruler is marked in millimeters.
Point B is closer to the 42 mm mark.

Answer: AB is about 42 millimeters long.
Length in Metric Units

B. Find the length of AB using the ruler.




Each centimeter is divided into fourths.
Point B is closer to the 4.5 cm mark.

Answer: AB is about 4.5 centimeters long.
A.   A
A. 2 mm               B.   B
B. 1.8 mm             C.   C
C. 18 mm    0%   0%
                      D.
                      0%
                           D
                           0%




            A




                 B




                      C




                           D
D. 20 mm
B.




                      A.   A
A. 1 cm               B.   B
B. 2 cm               C.   C
C. 2.5 cm   0%   0%
                      D.
                      0%
                           D
                           0%




            A




                 B




                      C




                           D
D. 3 cm
Length in Standard Units

A.




Each inch is divided into sixteenths. Point E is closer
to the 3-inch mark.
Length in Standard Units

B.
A.


A.


B.
               A.   A
C.             B.   B
               C.   C
D.   0%   0%
               D.
               0%
                    D
                    0%




     A




          B




               C




                    D
B.


A.


B.
               A.   A
C.
               B.   B
               C.   C
D.   0%   0%
               D.
               0%
                    D
                    0%




     A




          B




               C




                    D
Recall from Algebra that for any two real numbers a
and b, there is a real number n that is between a and
b such that a < n < b. This relationship also applies
to points on a line and is called betweeness of
points.
Find Measurements by Adding

Find XZ. Assume that the figure is not drawn to
scale.
Find BD. Assume that the figure is not               D
drawn to scale.
                                    50.4 mm
A. 16.8 mm

                          16.8 mm    C
B. 57.4 mm
                               B                    A.   A
C. 67.2 mm                                          B.   B
                                                    C.   C
D. 84 mm
                                          0%   0%   D.
                                                    0%   D
                                                         0%




                                         A




                                               B




                                                    C




                                                         D
Find Measurements by Subtracting

Find LM. Assume that the figure is not drawn
to scale.
Find TU. Assume that the figure is not
drawn to scale.
                                      3 in
                                                        V
A.       in.                      U
                             T

B.       in.
                                                   A.   A
C.       in.                                       B.   B
                                                   C.   C
D.       in.
                                         0%   0%
                                                   D.
                                                   0%
                                                        D
                                                        0%




                                         A




                                              B




                                                   C




                                                        D
Write and Solve Equations to Find Measurements

ALGEBRA Find the value of x and ST if T is between
S and U, ST = 7x, SU = 45, and TU = 5x – 3.
                            Draw a figure to represent
                            this situation.
ALGEBRA Find the value of n and WX if W is
between X and Y, WX = 6n – 10, XY = 17, and
WY = 3n.

A. n = 3; WX = 8


B. n = 3; WX = 9                               A.   A
                                               B.   B
C. n = 9; WX = 27
                                               C.   C
D. n = 9; WX = 44
                                     0%   0%
                                               D.
                                               0%
                                                    D
                                                    0%




                                     A




                                          B




                                               C




                                                    D
Congruent Segments

FONTS The Arial font is often used because it is easy
to read. Study the word time shown in Arial type.
Each letter can be broken into individual segments.
The letter T has two segments, a short horizontal
segment, and a longer vertical segment. Assume that
all segments overlap where they meet. Which
segments are congruent?
                    TIME
Answer: The five vertical segments in the letters T, I, M,
        and E are congruent. The four horizontal
        segments in T and E are congruent. The two
        diagonal segments in the letter M are
        congruent.
LEISURE ACTIVITIES The
graph shows the percent of
adults who participated in
selected activities. Suppose a
segment was drawn along the
height of each bar. Which
categories would have
segments that are congruent?               A.        A
A. barbecuing and beach                    B.        B
B. board games and museums                 C.        C
C. beach and picnic
                                           D.        D
D. zoo and board games           0%   0%   0%   0%




                                 A




                                      B




                                           C




                                                D
Drawings of geometric figures are created using measuring
tools such as a ruler and protractor.


Constructions are methods of creating figures without the
benefit of measuring tools. Generally, only a pencil,
straightedge and compass are used in constructions.


Sketches are created without the use of any of these tools.
Lesson 1.2 revised 2010

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Lesson 1.2 revised 2010

  • 1.
  • 2. Lesson 1-2 Warm-Up Name three collinear points. What is another name for AB? Name a line in plane Z. A. A Name the intersection of planes Z and W. B. B How many lines are in plane Z? C. C 0% 0% 0% D. 0% D A B C D
  • 3. Over Lesson 1–1 Name three collinear points. A. A, B, Q B. B, Q, T A. A C. A, B, T B. B C. C D. T, A, Q 0% 0% D. 0% D 0% A B C D
  • 4. Over Lesson 1–1 What is another name for AB? A. AA B. AT A. A C. BQ B. B C. C D. QB 0% 0% D. 0% D 0% A B C D
  • 5. Over Lesson 1–1 Name a line in plane Z. A. AT B. AW A. A C. AQ B. B C. C D. BQ 0% 0% D. 0% D 0% A B C D
  • 6. Over Lesson 1–1 Name the intersection of planes Z and W. A. BZ B. AW A. A B. B C. AB C. C D. BQ 0% 0% D. 0% D 0% A B C D
  • 7. Over Lesson 1–1 How many lines are in plane Z? A. 2 B. 4 A. A C. 6 B. B C. C D. infinitely many 0% 0% D. 0% D 0% A B C D
  • 8. Over Lesson 1–1 Which of the following statements is always false? A. The intersection of a line and a plane is a point. B. There is only one plane perpendicular to a given A. A plane. C. Collinear points are also B. B coplanar. C. C D. A plane contains an infinite 0% 0% D. 0% D 0% number of points. A B C D
  • 9. • line segment • betweenness of points • between • congruent segments • construction
  • 10. You identified and modeled points, lines, and planes. (Lesson 1–1) • Measure segments. • Calculate with measures.
  • 11. A line segment consists of two endpoints and all points between the endpoints. A segment with endpoints A and B can be named AB or BA. The length or measure of a segment always includes a unit of measure such as meter or inch.
  • 12. Length in Metric Units A. Find the length of AB using the ruler. The ruler is marked in millimeters. Point B is closer to the 42 mm mark. Answer: AB is about 42 millimeters long.
  • 13. Length in Metric Units B. Find the length of AB using the ruler. Each centimeter is divided into fourths. Point B is closer to the 4.5 cm mark. Answer: AB is about 4.5 centimeters long.
  • 14. A. A A. 2 mm B. B B. 1.8 mm C. C C. 18 mm 0% 0% D. 0% D 0% A B C D D. 20 mm
  • 15. B. A. A A. 1 cm B. B B. 2 cm C. C C. 2.5 cm 0% 0% D. 0% D 0% A B C D D. 3 cm
  • 16. Length in Standard Units A. Each inch is divided into sixteenths. Point E is closer to the 3-inch mark.
  • 17. Length in Standard Units B.
  • 18. A. A. B. A. A C. B. B C. C D. 0% 0% D. 0% D 0% A B C D
  • 19. B. A. B. A. A C. B. B C. C D. 0% 0% D. 0% D 0% A B C D
  • 20. Recall from Algebra that for any two real numbers a and b, there is a real number n that is between a and b such that a < n < b. This relationship also applies to points on a line and is called betweeness of points.
  • 21. Find Measurements by Adding Find XZ. Assume that the figure is not drawn to scale.
  • 22. Find BD. Assume that the figure is not D drawn to scale. 50.4 mm A. 16.8 mm 16.8 mm C B. 57.4 mm B A. A C. 67.2 mm B. B C. C D. 84 mm 0% 0% D. 0% D 0% A B C D
  • 23. Find Measurements by Subtracting Find LM. Assume that the figure is not drawn to scale.
  • 24. Find TU. Assume that the figure is not drawn to scale. 3 in V A. in. U T B. in. A. A C. in. B. B C. C D. in. 0% 0% D. 0% D 0% A B C D
  • 25. Write and Solve Equations to Find Measurements ALGEBRA Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3. Draw a figure to represent this situation.
  • 26. ALGEBRA Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n. A. n = 3; WX = 8 B. n = 3; WX = 9 A. A B. B C. n = 9; WX = 27 C. C D. n = 9; WX = 44 0% 0% D. 0% D 0% A B C D
  • 27.
  • 28. Congruent Segments FONTS The Arial font is often used because it is easy to read. Study the word time shown in Arial type. Each letter can be broken into individual segments. The letter T has two segments, a short horizontal segment, and a longer vertical segment. Assume that all segments overlap where they meet. Which segments are congruent? TIME Answer: The five vertical segments in the letters T, I, M, and E are congruent. The four horizontal segments in T and E are congruent. The two diagonal segments in the letter M are congruent.
  • 29. LEISURE ACTIVITIES The graph shows the percent of adults who participated in selected activities. Suppose a segment was drawn along the height of each bar. Which categories would have segments that are congruent? A. A A. barbecuing and beach B. B B. board games and museums C. C C. beach and picnic D. D D. zoo and board games 0% 0% 0% 0% A B C D
  • 30. Drawings of geometric figures are created using measuring tools such as a ruler and protractor. Constructions are methods of creating figures without the benefit of measuring tools. Generally, only a pencil, straightedge and compass are used in constructions. Sketches are created without the use of any of these tools.