Section 1.3 Measuring Segments

Students will be able to: find and compare lengths of segments Objective: Students will be able to: find and compare lengths of segments 1.3 Measuring Segments

coordinate distance congruent segments midpoint S=segment bisector Vocabulary: coordinate distance congruent segments midpoint S=segment bisector 1.3 Measuring Segments

This value is also AB, or the length between A and B. The distance between points A and B is the absolute value of the difference of their coordinates, or |a – b|. This value is also AB, or the length between A and B. 1.3 Measuring Segments

Problem 1: What is ST? What is UV? What is SV? 1.3 Measuring Segments

Problem 1 Solution: What is ST? What is UV? What is SV? 8 – (-4)  8 + 4 = 12 14 – 10 = 4 14 – (-4)  1 + 4 = 18 1.3 Measuring Segments

1.3 Measuring Segments

What algebraic expression represents EG? Problem 2: If EG = 59, what are EF and FG? What algebraic expression represents EG? What is the numeric value given for EG? How should you check to make sure that the segment lengths are correct? 1.3 Measuring Segments

What algebraic expression represents EG? Problem 2 Solution: If EG = 59, what are EF and FG? What algebraic expression represents EG? What is the numeric value given for EG? How should you check to make sure that the segment lengths are correct? (8x -14) + (4x + 1 )  12x - 13 59 12x - 13 = 59  12x = 72  x = 6 EF: 8x - 14 FG: 4x + 1 8(6) - 14 4(6) + 1 8(6) - 14  34 4(6) + 1  25 1.3 Measuring Segments

The symbol for congruent is ____________. When numerical expressions have the same value, you say that they are equal (=). Similarly, if two segments have the same length, then the segments are congruent segments. The symbol for congruent is ____________. 1.3 Measuring Segments

This means if AB = CD, then . You can also say that if , then AB = CD. 1.3 Measuring Segments

Is Segment AB congruent to Segment DE? Problem 3 Solution: Are and congruent? Is Segment AB congruent to Segment DE? 1.3 Measuring Segments

Problem 3: Are and congruent? AC =| – 2 – 5 | BD =| 3 – 10 | =| – 7 | =| – 7 | = 7 units = 7 units Is Segment AB congruent to Segment DE? YES. Since AC = BD. 1.3 Measuring Segments

That point, line, ray, or segment is called a segment bisector. The midpoint of a segment is a point that divides the segment into two congruent segments. A point, line, ray, or other segment that intersects a segment at its midpoint is said to bisect the segment. That point, line, ray, or segment is called a segment bisector. 1.3 Measuring Segments

Problem 4: Q is the midpoint of . What are PQ, QR, and PR? 1.3 Measuring Segments

Problem 4 Solution: Q is the midpoint of . What are PQ, QR, and PR? Midpoint = Halfway  Middle 6x – 7 = 5x + 1 PQ = 6x - 7 QR = 5x +1 PR = PR + QR - 5x -5x PQ = 6(8) - 7 QR = 5(8) +1 PR = 41 + 41 x – 7 = 1 PQ = 48 - 7 QR = 40 +1 + 7 + 7 PQ = 41 PR = 82 QR = 41 x = 8 1.3 Measuring Segments

Problem 4(b): U is the midpoint of . What are TU, UV, and TV? 1.3 Measuring Segments

Problem 4(b): U is the midpoint of . What are TU, UV, and TV? Midpoint = Halfway  Middle 8x + 11 = 12x - 1 TU = 8x + 11 UV = 12x -1 TV = TU + UV - 8x -8x TU = 8(3) + 11 UV = 12(3) -1 TV = 35 + 35 11 = 4x - 1 TU = 24 + 11 UV = 36 - 1 +1 + 1 TU = 35 TV = 70 UV = 35 12 = 4x 3 = x 1.3 Measuring Segments

Lesson Check 1.3 Measuring Segments

Lesson Check 1.3 Measuring Segments