1 2 Measuringand and Constructing Segments 1 2

1 -2 Measuring and Constructing Segments Warm Up Simplify. 1. -7 – (– 3)

1 -2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment.

1 -2 Measuring and Constructing Segments Vocabulary coordinate distance length between Holt Mc. Dougal

1 -2 Measuring and Constructing Segments A ruler can be used to measure the

1 -2 Measuring and Constructing Segments The distance between any two points is the

1 -2 Measuring and Constructing Segments Example 1: Finding the Length of a Segment

1 -2 Measuring and Constructing Segments Check It Out! Example 1 Find each length.

1 -2 Measuring and Constructing Segments Congruent segments are segments that have the same

1 -2 Measuring and Constructing Segments In order for you to say that a

1 -2 Measuring and Constructing Segments Example 3 A: Using the Segment Addition Postulate

1 -2 Measuring and Constructing Segments Example 3 B: Using the Segment Addition Postulate

1 -2 Measuring and Constructing Segments Example 3 B Continued M is between N

1 -2 Measuring and Constructing Segments Check It Out! Example 3 a Y is

1 -2 Measuring and Constructing Segments Check It Out! Example 3 b E is

1 -2 Measuring and Constructing Segments Check It Out! Example 3 b Continued E

1 -2 Measuring and Constructing Segments The midpoint M of AB is the point

1 -2 Measuring and Constructing Segments Example 5: Using Midpoints to Find Lengths D

1 -2 Measuring and Constructing Segments Example 5 Continued D is the midpoint of

1 -2 Measuring and Constructing Segments Check It Out! Example 5 S is the

1 -2 Measuring and Constructing Segments Check It Out! Example 5 Continued S is

1 -2 Measuring and Constructing Segments S is the midpoint of RT, RS =

1 -2 Measuring and Constructing Segments Classwork/Homework: • Chapter 1 Section 2 #s 1

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1 -2 Measuringand and. Constructing. Segments 1 -2 Measuring Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Warm Up Simplify. 1. -7 – (– 3) -4 2. |– 7 + 1| 6 Solve each equation. 3. 2 x + 3 = 9 x – 11 x=2 4. How many numbers are there between 2 and 7? a) 6 b) 5 c) 4 d) infinitely many Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Vocabulary coordinate distance length between Holt Mc. Dougal Geometry midpoint bisect segment bisector congruent segments

1 -2 Measuring and Constructing Segments A ruler can be used to measure the distance between two points. A point corresponds to one and only one number on a ruler. The number is called a coordinate. 3 is the coordinate at this point Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments The distance between any two points is the absolute value of the difference of the coordinates (this is the length of the segment). The notation AB without any symbols above it means the measure, or length, of AB. A a Holt Mc. Dougal Geometry B b AB = |a – b| or |b - a|

1 -2 Measuring and Constructing Segments Example 1: Finding the Length of a Segment Find each length. A. BC B. AC BC = |1 – 3| AC = |– 2 – 3| = |1 – 3| = |– 5| =2 =5 Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Check It Out! Example 1 Find each length. a. XY Holt Mc. Dougal Geometry b. XZ

1 -2 Measuring and Constructing Segments Congruent segments are 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. Symbol for congruency: ≅ Holt Mc. Dougal 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. Between does NOT mean in the middle!!!!!! Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 3 A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH 11 = 6 + GH – 6 5 = GH Holt Mc. Dougal Geometry Seg. Add. Postulate Substitute 6 for FG and 11 for FH. Subtract 6 from both sides. Simplify.

1 -2 Measuring and Constructing Segments Example 3 B: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO 17 + (3 x – 5) = 5 x + 2 3 x + 12 = 5 x + 2 – 2 3 x + 10 = 5 x – 3 x 10 = 2 x 2 2 5=x Holt Mc. Dougal Geometry Seg. Add. Postulate Substitute the given values Simplify. Subtract 2 from both sides. Simplify. Subtract 3 x from both sides. Divide both sides by 2.

1 -2 Measuring and Constructing Segments Example 3 B Continued M is between N and O. Find NO. NO = 5 x + 2 = 5(5) + 2 Substitute 5 for x. = 27 Simplify. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Check It Out! Example 3 a Y is between X and Z, XZ = 3, and XY = Find YZ. . Draw a Picture First!!!!!!! XZ = XY + YZ Seg. Add. Postulate Substitute the given values. Subtract Holt Mc. Dougal Geometry from both sides.

1 -2 Measuring and Constructing Segments Check It Out! Example 3 b E is between D and F. Find DF. DE + EF = DF (3 x – 1) + 13 = 6 x 3 x + 12 = 6 x – 3 x 12 = 3 x 12 3 x = 3 3 4=x Holt Mc. Dougal Geometry Seg. Add. Postulate Substitute the given values Subtract 3 x from both sides. Simplify. Divide both sides by 3.

1 -2 Measuring and Constructing Segments Check It Out! Example 3 b Continued E is between D and F. Find DF. DF = 6 x = 6(4) Substitute 4 for x. = 24 Simplify. Holt Mc. Dougal 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. A M B So if AB = 6, then AM = 3 and MB = 3. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 5: Using Midpoints to Find Lengths D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 Step 1 Solve for ED = DF 4 x + 6 = 7 x – 9 – 4 x D 7 x – 9 F x. D is the mdpt. of EF. Substitute 4 x + 6 for ED and 7 x – 9 for DF. Subtract 4 x from both sides. 6 = 3 x – 9 Simplify. +9 + 9 Add 9 to both sides. Simplify. 15 = 3 x Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 5 Continued D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 15 3 x = 3 3 x=5 Holt Mc. Dougal Geometry D 7 x – 9 Divide both sides by 3. Simplify. F

1 -2 Measuring and Constructing Segments Example 5 Continued D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 D 7 x – 9 F Step 2 Find ED, DF, and EF. ED = 4 x + 6 DF = 7 x – 9 = 4(5) + 6 = 7(5) – 9 = 26 Holt Mc. Dougal Geometry EF = ED + DF = 26 + 26 = 52

1 -2 Measuring and Constructing Segments Check It Out! Example 5 S is the midpoint of RT, RS = – 2 x, and ST = – 3 x – 2. Find RS, ST, and RT. R – 2 x S – 3 x – 2 T Step 1 Solve for x. S is the mdpt. of RT. RS = ST – 2 x = – 3 x – 2 Substitute – 2 x for RS and – 3 x – 2 for ST. +3 x Add 3 x to both sides. x = – 2 Holt Mc. Dougal Geometry Simplify.

1 -2 Measuring and Constructing Segments Check It Out! Example 5 Continued S is the midpoint of RT, RS = – 2 x, and ST = – 3 x – 2. Find RS, ST, and RT. R – 2 x S – 3 x – 2 T Step 2 Find RS, ST, and RT. RS = – 2 x = – 2(– 2) =4 Holt Mc. Dougal Geometry ST = – 3 x – 2 = – 3(– 2) – 2 =4 RT = RS + ST =4+4 =8

1 -2 Measuring and Constructing Segments S is the midpoint of RT, RS = 5 x, and RT = 8 x + 12. Find RS, ST, and RT. R 5 x Step 1: RT = RS + RT 8 x + 12 = 5 x + 8 x + 12 = 10 x - 8 x 12 = 2 x 6=x Holt Mc. Dougal Geometry S 8 x +12 T Then plug it in: Segment Addition RS=5(6)=30 RS = RT 5 x ST=30 Combine Like Terms RT = 8(6)+12=60 Subtract 8 x to both sides Simplify Divide by -12 to both sides

1 -2 Measuring and Constructing Segments Classwork/Homework: • Chapter 1 Section 2 #s 1 -10 all, 11 -25 odd, 31, 33 Holt Mc. Dougal Geometry