1-2 Measuring and Constructing Segments
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1 1-2 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz
2 Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments.
3 Vocabulary coordinate midpoint distance bisect length segment bisector construction between congruent segments
4 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. The following postulate summarizes this concept.
5
6 The distance between any two points is the absolute value of the difference of the coordinates. If the coordinates of points A and B are a and b, then the distance between A and B is a b or b a. The distance between A and B is also called the length of AB, or AB. A a B b AB = a b or b - a
7 Example 1: Finding the Length of a Segment Find each length. A. BC B. AC BC = 1 3 AC = 2 3 = 1 3 = 2 = 5 = 5
8 Find each length. Check It Out! Example 1 a. XY b. XZ
9 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.
10 You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge.
11 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.
12 Example 3A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH 11 = 6 + GH = GH Seg. Add. Postulate Substitute 6 for FG and 11 for FH. Subtract 6 from both sides. Simplify.
13 Example 3B: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO 17 + (3x 5) = 5x + 2 3x + 12 = 5x x + 10 = 5x 3x 3x 10 = 2x = x Seg. Add. Postulate Substitute the given values Simplify. Subtract 2 from both sides. Simplify. Subtract 3x from both sides. Divide both sides by 2.
14 Example 3B Continued M is between N and O. Find NO. NO = 5x + 2 = 5(5) + 2 = 27 Substitute 5 for x. Simplify.
15 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.
16 Example 5: 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. ED = DF D is the mdpt. of EF. 4x + 6 = 7x 9 Substitute 4x + 6 for ED and 7x 9 for DF. 4x 4x 6 = 3x 9 Subtract 4x from both sides. Simplify Add 9 to both sides. 15 = 3x Simplify.
17 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 7x 9 F 15 3x = 3 3 Divide both sides by 3. x = 5 Simplify.
18 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 7x 9 F Step 2 Find ED, DF, and EF. ED = 4x + 6 = 4(5) + 6 = 26 DF = 7x 9 = 7(5) 9 = 26 EF = ED + DF = = 52
19 Lesson Quiz: Part I 1. M is between N and O. MO = 15, and MN = 7.6. Find NO S is the midpoint of TV, TS = 4x 7, and SV = 5x 15. Find TS, SV, and TV. 25, 25, Sketch, draw, and construct a segment congruent to CD. Check students' constructions
20 Lesson Quiz: Part II 4. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch. If M is the midpoint of KL, then M, K, and L are collinear. Always K M L
1-2 Measuring and Constructing Segments
1-2 Measuring and Constructing Segments Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance
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