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Measuring Segments & Angles, Absolute Value Expressions, and Equations

This lesson covers how to simplify absolute value expressions, measure segments using the distance formula, and solve equations involving segments. It also introduces the concept of angles and their measurements. Includes practice problems.

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Measuring Segments & Angles, Absolute Value Expressions, and Equations

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  1. 1-4 Warmup Simplify each absolute value expression. 1) –62) 3.53) 7 – 10 4) –4 – 25) –2 – (–4)6) –3 + 12 Solve each equation. 7. x + 2x – 6 = 6 8. 3x + 9 + 5x = 81 9. w – 2 = –4 + 7w

  2. Lesson 1-4: Measuring Segments & Angles The location of a point. Objects that are the same shape and size A part of a line from one point to another A point that divides a segment into two equal segments

  3. Measures with segments: Distance between two points is the absolute value of the difference between their coordinates. A B -1 0 1 Distance from A to B is or Both equal 9!

  4. Example 3-1a Use the number line to find QR. The coordinates of Q and R are –6 and –3. Distance Formula Simplify. Answer: 3

  5. (cont’d) • Symbol: AB means the segment: AB (without symbol) means the length • Congruent segments • When 2 segments are the same length, we write… or A C B D

  6. Small segment Small segment Whole segment • Segment Addition: “parts of a segment add to the whole” ___________ + ___________ = ____________ • Midpoint • Forms 2 congruent segments on a segment (Cuts it in half!) • Equations: ________ = _________ ________ = ½ ● ________ These red marks indicate segments AM and BM are the same. A M B Small segment Other small segment Small segment Whole segment

  7. Multiple-Choice Test ItemWhat is the measure of ifBis the midpoint of ? A 1 B 3 C 5 D 10 Example 3-5e Answer: D

  8. Formed by two rays or segments that share an endpoint An angle whose measure is smaller than a “corner” An angle whose measure is a “corner” - 900 An angle whose measure is greater than a “corner” An angle whose measure is a straight line - 1800

  9. Angles A vertex 1 sides B C Parts: Sides: rays BA and BC Vertex: point B Naming: 3 letters (all angles): 1 letter: 1 number: Tracing these letters makes the angle. or Only when there is exactly 1 angle at the vertex!

  10. a. Name all angles that have X as a vertex. b. Name the sides of 3. Answer: c. Write another name for 3. Example 4-1d Answer:1, 2, 3, and RXB or RXN Answer:AXB, AXN, NXA, BXA

  11. Types of angles • Acute – “small” • Measures 00 - 890 • Right – “right turn” • Measures 900 • Obtuse – “obese” • Measures 910 - 1790 • Straight • Measures 1800 This red box indicates a right angle of 90 degrees.

  12. Example ; . Find We can write an equation by thinking: small + small = whole A 1 2 B C

  13. Assignment: Practice 1-4

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