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Warm Up Simplify. 1.7 – (–3)2. –1 – (–13)3. |–7 – 1| Solve each equation. 4. 2x + 3 = 9x – 115. 3x = 4x – 5 6. How many numbers are there between and ?
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Warm Up Simplify. 1.7 – (–3)2. –1 – (–13)3. |–7 – 1| Solve each equation. 4. 2x + 3 = 9x – 115. 3x = 4x – 5 6. How many numbers are there between and ? 10128 x = 2x = 5 Infinitely many
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coordinatemidpoint distancebisect lengthsegment bisector construction between congruent segments Vocabulary
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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.
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The distance between any two points is always positive. Therefore, we can say that the distance between the points is the absolute value of the difference of the coordinates. AB = |a – b| or |b - a| A a B b 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.
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Congruent segments are segments that have the same length. Use compass only – no ruler – to create congruent segments Create congruent segments on your notes (lightly show tick mark).
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Key Concept – Be careful … PQ represents a number (or distance) while represents a geometric figure (line segment). Be sure to use equality for numbers (PQ = PQ) while we use congruence for figures
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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 (which is to say they are collinear) and AB + BC = AC.
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M is between N and O. Find NO. The key to solving this is the segment addition postulate which says than NM + MO = NO
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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. Bisect a segment with a compass …
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Lesson Quiz 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 2.S is the midpoint of, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. 3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.
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Lesson Quiz 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 2.S is the midpoint of, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. 3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x. NO = 22.6
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Lesson Quiz 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 2.S is the midpoint of, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. 3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x. TS = 25, SV = 25 and TV = 50
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Lesson Quiz 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 2.S is the midpoint of, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. 3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x. x = 3
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Assignment today is page 17: 12-15, 20-29, 35-41 and 48-49. Remember that homework help is always available at http://www.thinkcentral.com/index.htm http://www.thinkcentral.com/index.htm Today’s keyword is “MG7 1-2”.
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