Measuring Segments 1-3 (New Orleans Style). Measuring Segments 1-3 (New Orleans Style)

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Presentation transcript:

Measuring Segments 1-3 (New Orleans Style)

TO LEARN MATHEMATICS IS TO LEARN LANGUAGE

To find and compare lengths of segments 1-3 Measuring Segments Objective : To find and compare lengths of segments

ALGEBRA GEOMETRY A B M A B Segment AB

Take Cornell Notes… The Ruler Postulate: Every point on a line can be paired with a real number. This makes a one to one correspondence between the points on the line and the real numbers. Coordinate: The real number that corresponds to a point. __________________________________________ The Ruler Postulate allows you to measure lengths of segments using a given unit and to find distances between points on a line.

How long is this PoBoy? How do you know that? 0 + 12 UNITS = 12

Take CornellNote… AB in Geometry translates to a distance or length│b - a│ in Algebra where a and b are coordinates. This is because of the Ruler Postulate. (Remember a coordinate is the real number that corresponds to a point) A B a b AB in Geometry AB =│b - a│in Algebra

Problem: What is the length of ST on the given line? ALGEBRA CONNECTION Problem: What is the length of ST on the given line? S T U V (Think…What is the problem asking for? What is length? The coordinate of S is -4. The coordinate of T is 8. ST = │ b – a │ Ruler Postulate ST = │8 – (-4) │ substitution ST = │12│ addition ST = 12 Practice on your own…What is the length of UV and SV?

If we cut a poboy in two parts, Then what is the relationship between the entire poboy and its two parts?

Take Note… Segment Addition Postulate: If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C AB BC AC

Problem: If EG = 59, what are EF and FG? ALGEBRA CONNECTION Problem: If EG = 59, what are EF and FG? E F G 8x - 14 4x + 1 Think…What is given? What is the problem asking for? How do you find it? Is there a relationship between EG ,EF ,and FG that would help you? EF + FG = EG Segment Addition Postulate (8x – 14) + (4x + 1) = 59 Substitution 12x – 13 = 59 Combining like terms 12x = 72 Adding 13 to both sides x = 6 Dividing 12 on both sides

Is there a relationship between The two parts of the po-boy?

What is B and why? What is l and Why? Take Note… Congruent segments: segments that have the same length. (≅) (∣, ∣∣, ∣∣∣) Midpoint: a point that divides a segment into two congruent segments. Segment Bisector: a point, line, ray, or other segment that intersects a segment at its midpoint. l A B C │ What is B and why? What is l and Why?

Problem: Are AC and BD congruent? ALGEBRA CONNECTION Problem: Are AC and BD congruent? A B C D E (THINK…What type of geometric objects are AC and BD? What does it mean for AC and BD to be congruent? Can we express this algebraically in order to help find out if AC and BD are congruent? AC = │ 5 – (-2)│= │7│= 7 BD = │ 10 – 3 │= │7│= 7 Yes, they are congruent. Practice on your own…Is AB congruent to DE?

Problem: Q is the midpoint of PR. What are PQ, QR, and PR? ALGEBRA CONNECTION Problem: Q is the midpoint of PR. What are PQ, QR, and PR? P Q R 6x – 7 5x + 1 Think…What is given? What do we need to find? What can we conclude from Q being the midpoint of PR? How do we express that algebraically? PQ = QR Definition of a midpoint 6x – 7 = 5x + 1 Substitution x – 7 = 1 Subtracting 5x on both sides x = 8 Adding 7 to both sides On your own…Since we found that x = 8, Find PQ, QR, and PR.

THE END