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Segment Addition

Segment Addition. Segment addition problems can sometimes seem confusing, but as long as you remember that the two smaller parts make up the whole, you will be in good shape! This means:. one small part + other small part = whole segment. Segment Addition.

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Segment Addition

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  1. Segment Addition Segment addition problems can sometimes seem confusing, but as long as you remember that the two smaller parts make up the whole, you will be in good shape! This means: one small part + other small part = whole segment

  2. Segment Addition one small part + other small part = whole segment AC C B A AB BC AB + BC = AC This is the Segment Addition Postulate

  3. Segment Addition AC C B A AB BC AB + BC = AC Example 1: If AB = 23 and BC = 47, find AC

  4. Segment Addition AC C B A 23 47 AB + BC = AC Example 1: If AB = 23 and BC = 47, find AC + 47 = AC 70 = AC 23

  5. Segment Addition 60 C B A 4x + 5 15 AB + BC = AC Example 2: If AB = 4x + 5, BC = 15, and AC = 60 find x. + 15 = 60 4x + 5 4x + 20 = 60 4x = 40 x = 10

  6. Segment Addition 58 C B A 28 ? AB + BC = AC Example 3: If AB = 28 and AC = 58 find BC. + BC = 58 + x = 58 28 28 x = 30 Which means BC = 30

  7. Segment Addition AB + BC = AC 5x - 12 C B A 2x - 8 -x + 24 Example 4: If AB = 2x – 8, BC = - x + 24, and AC = 5x – 12, find AC. 2x - 8 + - x + 24 = 5x - 12 x + 16 = 5x – 12 16 = 4x – 12 Now that we know x = 7 we can easily find AC by replacing 7 with x in 5x – 12. 5x – 12 = AC 5(7) – 12 = AC 35 – 12 = AC 23 units = AC 28 = 4x 7 = x

  8. Midpoint of a Segment Midpoint: • We have learned that if A, B, and C are collinear then AB + BC = AC • If AB = BC then B is called the midpoint of AC, and we can put in the tic marks to show that AB and BC are congruent A B C A B C

  9. Midpoint of a Segment A B C AB + BC = AC Example 1: B is the midpoint of AC. If AC = 115 and AB = 5x – 10, find x. AB + BC = AC 5x – 10 + BC = 115 5x – 10 + 5x – 10 = 115 10x – 20 = 115 10x = 135 x = 13.5

  10. Midpoint of a Segment Example 2: B is the midpoint of AC. Find x, AB, BC, and AC. A B C AB = BC 4x + 12 = 5x – 3 4x + 15 = 5x 15 = x 4x + 12 5x - 3

  11. Midpoint of a Segment Example 2: B is the midpoint of AC. Find x, AB, BC, and AC. A B C AB = BC 4x + 12 = 5x – 3 4x + 15 = 5x 15 = x 4x + 12 5x - 3 4x + 12 = AB 4(15) + 12 = AB 60 + 12 = AB 72 = AB 72 = BC AB + BC = AC 72 + 72 = AC 144 = AC

  12. Segment Bisector Bicycle has TWO wheels that are the same size. Biplane has TWO wings that are the same size. So what do a biplane and a bicycle have in common with a segment bisector?

  13. Segment Bisector A segment Bisector ensures the segment has been divided into TWO parts that are the same size. The bisector goes through the segment midpoint and we know that: Line m is the segment bisector B is the midpoint of AC m C B A The marks indicate that each part is congruent

  14. Perpendicular Segment Bisector A perpendicular segment Bisector is a segment bisector that runs perpendicular to the segment and passes through the midpoint of the segment. • Line m is the perpendicular segment bisector • B is the midpoint of AC m C B A The marks indicate that each part is congruent

  15. Segment Addition with Bisectors m 50 C B A 2x - 4 BC Example 4: If m is a bisector of AC, AB = 2x – 4, AC = 50, find BC. Recall: AB + BC = AC AB + BC = AC 2x – 4 + BC = 50

  16. Segment Addition with Bisectors m 50 C B A 2x - 4 BC Example 4: If m is a bisector of AC, AB = 2x – 4, AC = 50, find BC. Recall: AB + BC = AC AB + BC = AC 2x – 4 + BC = 50 2x – 4 + 2x – 4 = 50 4x – 8 = 50 4x = 58 x = 14.5

  17. Segment Addition with Bisectors m 50 C B A 2x - 4 BC Example 4: If m is a bisector of AC, AB = 2x – 4, AC = 50, find BC. Recall: AB + BC = AC AB + BC = AC 2x – 4 + BC = 50 2x – 4 + 2x – 4 = 50 4x – 8 = 50 4x = 58 x = 14.5 2x – 4 = BC 2(14.5) – 4 = BC 29 – 4 = BC 25 = BC

  18. Example 5: Given , find JK. mJK = mLM -2x + 33 = 6x - 23 33 = 8x – 23 56 = 8x 7 = x JK = -2x + 33 JK = -2(7) + 33 JK = 19

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