Transcript Holt McDougal Geometry 1-2

1-2 Measuring and Constructing Segments
1.1 Exit Ticket: Part 1 Answers
1. Two opposite rays.
CB and CD
2. A point on BC.
Possible answer:
B,C, D
3. The intersection of plane N and plane T.
Possible answer: BD
4. A plane containing E, D, and B.
Plane T
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Exit Ticket: Part II Answers
Draw each of the following.
5. a line intersecting a plane at one point
6. a ray with endpoint P that passes through Q
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Objectives
1. Use Segment Addition Postulate and Midpoint
2. Construct Congruent segment and Midpoint
AB
Length of AB (distance between A & B)
AB
line segment AB
AB
line AB
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Find the distance between two points or the length of the segment
ExampleFind the length of EF, FC, DC
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Find the distance between two points or the length of the segment
You PracticeFind the length of DB and DC
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Congruent segments: segments that have the same length.
In the diagram, PQ = RS, so you can write:
PQ  RS.
This is read as:
“segment PQ is congruent to segment RS.”
Tick marks are used in a figure to show congruent segments.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
In order for you to say that a point B is between
two points A and C, all three points must lie on the
same line, and AB + BC = AC.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Example 1A: Using the Segment Addition Postulate
G is between F and H, FG = 6, and FH = 11.
Find GH.
1. Draw picture
2. Write equation based on picture
.
3. Solve
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Example 1B: Using the Segment Addition Postulate
R is between T and M, RT = 7, and RM = 12.
Find TM.
1. Draw picture
2. Write equation based on picture
.
3. Solve
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Check It Out! Example 1
Y is between X and Z, XZ = 15, and XY =2
Find YZ.
XZ = XY + YZ
Holt McDougal Geometry
.
1-2 Measuring and Constructing Segments
Challenge: Using the Segment Addition Postulate
M is between N and O.
Find NO.
Seg. Add. Postulate
Substitute the given values
Simplify.
Subtract 2 from both sides.
Subtract 3x from both sides.
Divide both sides by 2.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Challenge: Using the Segment Addition Postulate
E is between D and F.
Find DF.
Seg. Add. Postulate
Substitute the given values
Simplify.
Subtract 3x from both sides.
Divide both sides by 3.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Midpoint:
Bisect:
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
The midpoint M of AB is the point that
bisects, or divides, the segment into two
congruent segments.
If M is the midpoint of AB, then AM = MB.
So if AB = 6, then AM = 3 and MB = 3.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Construct Midpoint and segment bisector
Math Open Reference
http://www.mathopenref.com/tocs/constructionst
oc.html
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Example 2A: Using the Midpoint
S is the midpoint of JK, and SJ = 4. Find JK
1. Draw picture
2. Write equation based on picture
.
3. Solve
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Example 2B: Using the Midpoint
B is the midpoint of AC, and AB = 22. Find BC
1. Draw picture
2. Write equation based on picture
.
3. Solve
Holt McDougal Geometry
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
D
7x – 9
F
Step 1 Solve for 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.
Holt McDougal Geometry
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
D
7x – 9
F
Step 1 Solve for 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.
Holt McDougal Geometry
1-2 Measuring and Constructing Segments
Check It Out! Example 3
S is the midpoint of RT, RS = –2x, and
ST = –3x – 2. Find RS, ST, and RT.
R
–2x
S
–3x – 2
T
Step 1 Solve for x.
S is the mdpt. of RT.
RS = ST
–2x = –3x – 2 Substitute –2x for RS and –3x – 2 for ST.
+3x
+3x
x = –2
Holt McDougal Geometry
Add 3x to both sides.
Simplify.
1-2 Measuring and Constructing Segments
HW
• Pg 17, 1-7, 17,18
Holt McDougal Geometry