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1.2 Segments and Their Measures

1.2 Segments and Their Measures. Warm Up Simplify. 7 – (–3) 2. –1 – (–13) 3. | –7 – 1| Solve each equation. 4. 2 x + 3 = 9 x – 11 5. 3 x = 4 x – 5. 6. How many numbers are there between and ?. 1.2 Segments and Their Measures. Objectives.

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1.2 Segments and Their Measures

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  1. 1.2 Segments and Their Measures Warm Up Simplify. • 7 – (–3) 2. –1 – (–13) 3. |–7 – 1| Solve each equation. 4. 2x + 3 = 9x – 11 5. 3x = 4x – 5 6. How many numbers are there between and ?

  2. 1.2 Segments and Their Measures Objectives Apply the Segment Addition Postulate. Construct congruent segments.

  3. Congruent segments are segments that have the same __________. • In the diagram, PQ = RS, so you can write . This is read as “segment PQ is congruent to segment RS.” Tick marks are used in a figure to show congruent segments. length

  4. Segment Addition Postulate If B is between A and C, Then AB + BC = AC A BC AB + BC = AC

  5. Example 1 G is between F and H, FG = 6, and FH = 11. Draw the picture, then find GH.

  6. Example 2 M is between N and O. Find x. Find NO.

  7. Example 3 Eis between D and F. DE = 3x – 1, EF = 13, and DF = 6x. Draw a picture. Find x. Find DF.

  8. Example 4 Dis the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Draw a picture. Find ED, DF, and EF.

  9. Example 5 Sis the midpoint of RT, RS = –2x, and ST= –3x – 2. Draw a picture and find RS, ST, and RT.

  10. Example 6 The map shows the route for a race. You are at X, 6000 ft from the first checkpoint C. The second checkpoint D is located at the midpoint between C and the end of the race Y. The total race is 3 miles. How far apart are the 2 checkpoints?

  11. There are three ways to represent a geometric figure. Sketch – a free hand copy of a figure. Drawing – using a ruler and protractor to copy a figure. Construction – using a compass and straight edge to copy a figure. A ruler shows that two segments are approximately the same length, but a construction shows that two segments are precisely the same length.

  12. Example 7 Sketch, draw, and construct a segment congruent to . Step 1 Estimate and sketch. Estimate the length of and sketch approximately the same length. Step 3 Construct and compare. Use a compass and straightedge to construct congruent to . Step 2 Measure and draw. Use a ruler to measure . appears to be _____ in. Use a ruler to draw to have length _____ in.

  13. 2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. 1.2 Quiz 1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

  14. 3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

  15. 4. Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch. If M is the midpoint of KL, then M, K, and L are collinear.

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