Entry Task
• 1) How many numbers are there between
and ? Explain.
• 2) Name a point, line, ray and segment in the
following.
LT: I can use number operations to find and
compare lengths of segments
Geometry
Chapter 1.3
Segments, Rays, Parallel Lines and
Planes
Learning Target
I can use number operations to find
and compare lengths of segments
LT: I can use number operations to find and
compare lengths of segments
Definitions Reviewed…
• Segment
– Part of a line consisting of two endpoints and all points in
between
• Ray
– Part of a line consisting of one endpoint and all points of the
line on one side of the endpoint
• Opposite Rays
– Two collinear rays with the same endpoint
• These rays always form a line
LT: I can use number operations to find and
compare lengths of segments
Definitions Cont…
• Congruent Segments
– Segments with the same length
• Midpoint
– A point that divides a segment into two congruent
segments
• Segment Bisector
– A pt. line, ray or segment that divides a segment
LT: I can use number operations to find and
compare lengths of segments
• This is explaining that you can use a ruler to
measure things.
LT: I can use number operations to find and
compare lengths of segments
Think about it….
• If from Joe’s house to Mike’s house is 4 miles,
Mike’s house to Ann’s house is 3 miles.
Assuming Mike lives on the same road as Joe
and Ann, how far is it from Joe’s to Ann’s?
LT: I can use number operations to find and
compare lengths of segments
1-2 Measuring and Constructing Segments
Check It Out! Example 1
Find each length.
b. XZ
a. XY
Holt Geometry
LT: I can use number operations to
find and compare lengths of segments
1-2 Measuring and Constructing Segments
Example 2 Continued
M is between N and O.
Find NO.
NO = 5x + 2
Holt Geometry
= 5(5) + 2
Substitute 5 for x.
= 27
Simplify.
LT: I can use number operations to
find and compare lengths of segments
1-2 Measuring and Constructing Segments
Example 2B Continued
M is between N and O.
Find NO.
NO = 5x + 2
Holt Geometry
= 5(5) + 2
Substitute 5 for x.
= 27
Simplify.
LT: I can use number operations to
find and compare lengths of segments
1-2 Measuring and Constructing Segments
Example 3: Using Midpoints to Find Lengths
D is the midpoint of EF, ED = 4x + 6, and
DF = 7x – 9. Find ED, DF, and EF.
E
4x + 6
Step 1 Solve for
ED = DF
4x + 6 = 7x – 9
–4x
–4x
6 = 3x – 9
+9
+9
15 = 3x
Holt Geometry
D
7x – 9
F
x.
D is the mdpt. of EF.
Substitute 4x + 6 for ED and 7x – 9 for DF.
Subtract 4x from both sides.
Simplify.
Add 9 to both sides.
Simplify.
LT: I can use number operations to
find and compare lengths of segments
1-2 Measuring and Constructing Segments
Example 5 Continued
D is the midpoint of EF, ED = 4x + 6, and
DF = 7x – 9. Find ED, DF, and EF.
E
4x + 6
15 3x
=
3
3
x=5
Holt Geometry
D
7x – 9
Divide both sides by 3.
Simplify.
LT: I can use number operations to
find and compare lengths of segments
F
1-2 Measuring and Constructing Segments
Example 5 Continued
D is the midpoint of EF, ED = 4x + 6, and
DF = 7x – 9. Find ED, DF, and EF.
E
4x + 6
D
F
7x – 9
Step 2 Find ED, DF, and EF.
ED = 4x + 6
DF = 7x – 9
= 4(5) + 6
= 7(5) – 9
= 26
= 26
Holt Geometry
EF = ED + DF
= 26 + 26
= 52
LT: I can use number operations to
find and compare lengths of segments
Homework #2
• P. 24 #8,12,16,19,20-22,35,37,38,39,40
• Challenge – p. 25 #42
LT: I can use number operations to find and
compare lengths of segments