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Geometry

Geometry. Chapter 1 1-2 measuring and constructing segments. Warm up. 1. Name three collinear points 2. Name two opposite rays 3. A plane containing E , D , and B . Draw each of the following 4. a line intersecting a plane at one point

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Geometry

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  1. Geometry Chapter 1 1-2 measuring and constructing segments

  2. Warm up • 1. Name three collinear points • 2. Name two opposite rays • 3.A plane containing E, D, and B. Draw each of the following 4. a line intersecting a plane at one point 5. a ray with endpoint P that passes through Q

  3. Warm up answers • 1. Name three collinear points • Answer: B,C and D • 2. Name two opposite rays • Answer: CB and CD • 3. A plane containing E, D, and B. Plane T Draw each of the following 4. a line intersecting a plane at one point 5. a ray with endpoint P that passes through Q

  4. Objectives • Students will be able to: • Use length and midpoint of a segment. • Construct midpoints and congruent segments.

  5. 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. The following postulate summarizes this concept.

  6. A B AB = |a – b| or |b - a| a b Measuring and constructing segments • 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.

  7. Example 1 • Find each length • AB AC • AB=|-2-1| AC=|-2-3| • =|-3|=3 =|-5|=5

  8. Example 2 • Check it out Ex. 1 page 13 Find each length.

  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. 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 3 • If B is between A and C and AB is 7 and AC is 20. Find the length of BC. Answer: AC=AB+BC segment addition postulate 20=7+BC substitute the values of AC and AB -7 -7 then solve for BC 13= BC

  13. Example 4 • Let’s say S is in between R and T and RS= x+4 and ST=2x+6. Find RT. • Solution: • RT=RS+ST using segment addition postulate add common terms and simplify

  14. Example 5 • Let B be in between A and C. If AB =4x-5 and BC= 5x+7. If AC= 47. Find x. • Solution: • AC=AB+BC using adding segment postulate substitute AB,BC and AC combine like terms and simplify simplify and solve for x -2 -2 solve for x

  15. Midpoint of a segment • What is a Midpoint of a segment? • Solution: • The midpointM 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. • A segment bisector is any ray , segment or line that intersects the segment at its midpoint. It divides the segment into two equal parts just like the midpoint.

  16. –4x–4x Example 6 • D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. • Solution: • ED = DF D is the mdpt. of EF. • 4x + 6 = 7x – 9 Substitute 4x + 6 for ED and 7x – 9 forDF • Subtract 4x from both sides. • 6 = 3x – 9 Simplify. • +9 +9 • solve for x • 5=x or x=5

  17. Homework • Chapter 1-2 • Page 17 14, 15 • Page 18 31-33 • Page 19 36-39

  18. Closure • Today we learned about constructing segments, segment addition postulate and the midpoint • Tomorrow we are going to continue with section 3.

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