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1. Foundations of Geometry
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United States of AmericaVirginia
Geometry

1.04 Line segments and constructions

Lesson
Practice
Adaptive
Worksheet
What do you remember?
1

Use the diagram to find each segment length.

Segment A B with points C, D, E, and F on A B. A B is above a number line ranging from negative 4 to 5. Point A lines up with negative 3 on the number line, C lines up with negative 2, D lines up with O, E lines up with 1, F lines up with 2, and B lines up with 4.
a
AC
b
AE
c
EF
d
FB
e
DB
f
AB
2

Write an equivalence statement using the segment addition postulate, then find the length of the indicated segment.

a

CE

Segment C E with point D on C E. Segment C D has a length of 9, and D E has a length of 19.
b

GH

Segment F H with point G on F H. Segment F G has a length of 19, and F H has a length of 34.
3

Use the diagrams provided to find the indicated length.

a

PR

Segment P Q with point R the midpoint of P Q. P Q has a length of 10.2 millimeters.
b

AB

Segments A B and Y X intersecting at point Z. Z is the midpoint of A B. The length of A Z is 25.7 centimeters.
4

Use the diagram and the given information to answer each question.

  • H is the midpoint of \overline{LI}.

  • \overleftrightarrow{GM} bisects segment EJ.

Three intersecting line segments A B, E F, and G M. A B intersects G M at point L. E F intersects G M at point I. A B intersects E F at point J. A fourth segment C D is drawn. C D intersects G M at point H. C D intersects A B at point K. Segment L K is congruent to segment K J.
a

List all pairs of congruent segments.

b

Identify two additional segments that have been bisected, and the line which bisects them.

c

Identify two additional midpoints.

5

Which type of construction is illustrated in the figure?

The image shows 2 compass. The 1st compass shows line segment AB and 2nd compass shows ray with line segment CD. Ask your teacher for more information.
A

The bisection of \overleftarrow{CD}

B

A line segment congruent to \overline{AB}

C

A line segment congruent to \overline{CD}

D

An angle congruent to \angle ABD

6

Construct a line segment PC such that \overline{PC} \cong \overline{AB}.

a
Segment A B and a point P not on A B.
b
Segment A B and a point P not on A B.
7

Use a construction to locate the midpoint of \overline{MP}. Describe each step of your construction.

Segment M P.
Let's practice
8

Consider the segment shown in the diagram:

Segment A B with points C, D, E, and F on A B. A B is above a number line ranging from negative 4 to 5. Point A lines up with negative 3 on the number line, C lines up with negative 2, D lines up with O, E lines up with 1, F lines up with 2, and B lines up with 4.
a

Determine which segments are congruent to \overline{AC}.

b

Determine which segments are congruent to \overline{AE}.

c

If a point G was added at -1, determine how many additional congruent segments you would find in parts (a) and (b).

d

Identify all midpoints in the diagram and the segments they bisect.

9

Use the segment addition postulate to find the unknown length.

a

Given: JK = 5 x + 2,\,KL = 7 x + 4 and JL = 42. Find KL.

Segment J L with point K on J L.
b

Given: JT = 5 x + 5,\,CT = 76 and CJ = 4 x + 8. Find JT.

Segment C T with point J on C T.
10

Suppose the point B lies on the segment \overline{CD} between the points C and D.

a

If CD = 4 x,\,BD = 2 x and CB = 12, find the length of \overline{BD}.

b

If CB = 3 x - 6,\,BD = 4 x + 3 and CD = 18, find the length of \overline{CB}.

11

In the diagram, M is the midpoint of \overline{KL}. Find the length ML.

Segment K L with point M on K L. Segment K M has a length of 5 x plus 6, and M L has a length of 8 x minus 21.
12

In the diagram, Y is the midpoint of \overline{XZ}. Find the length XZ.

Segment X Z with point Y on X Z. Segment X Y has a length of 5 k minus 2, and Y Z has a length of 18 plus 3 k.
13

Q is the midpoint of \overline{PR}, with PQ = 3 x - 8 and QR = 2 x + 3.

Determine the length PQ.

14

\overline{XY} bisects \overline{UV} at W.

If UW = 8 x + 5, find an expression for the length UV.

15

Construct a segment that is half the length of AB with an endpoint on X. Describe each step of your construction.

Segment A B and a point X not on A B.
16

Construct a new line segment whose length is equal to AB + DE.

Segment A B, and a shorter segment D E.
Let's extend our thinking
17

Given that points X,\,Y, and Z are collinear, and that XY = 12 and XZ = 18, determine the possible lengths for YZ.

Draw diagrams that support your solution.

18

Given that AB=10,\,BC=5, and AC=12 determine if points A,\,B, and C are collinear. Explain.

19

Two students use the ruler postulate to measure the length of \overline{QB} in the diagram.

Line A B with points P and Q on A B.

Student A:

Line A B with points P and Q on A B. A B is below a number line ranging from negative 10 to 10. Point A lines up with the point between negative 5 and negative 4, P lines up with 0, Q lines up with 3, and B lines up with 9.
QB = \left \vert \ 9-3 \right \vert = \left \vert \ 6 \right \vert = 6

Student B:

Line A B with points P and Q on A B. A B is below a number line ranging from negative 10 to 10. Point A lines up with negative 8, P lines up with the point between negative 4 and negative 3, Q lines up with 0, and B lines up with 6.
QB = \left \vert \ 6-0 \right \vert = \left \vert \ 6 \right \vert = 6

Explain why both students have the same solution for the length of \overline{QB}.

20

LeeAnn wants to divide her paper into four columns of equal width without making any folds. Describe the compass and straight edge constructions LeeAnn could use to accomplish her goal.

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