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WARM UP!

Chicago, Bloomington, Springfield. ANSWER. WARM UP!. Find three cities on this map that appear to be collinear. Front Side – True or False. Back Side. Use the diagram to answer the questions. 9. Name one pair of opposite rays. ____________ & ____________. Opposite Rays

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WARM UP!

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  1. Chicago, Bloomington, Springfield ANSWER WARM UP! Find three cities on this map that appear to be collinear.

  2. Front Side – True or False

  3. Back Side Use the diagram to answer the questions. 9. Name one pair of opposite rays. ____________ & ____________ • Opposite Rays • Share the same end point • The 2 rays are on the same line • They go in opposite directions

  4. Lesson 1.2 Use Segments and Congruence

  5. CongruentSegments: exactly the same size and length I I • XY= PQ • segment XY is congruent to segment PQ

  6. Between: A point is between 2 points if it is on the line (collinear with) that connects those two points.

  7. Broken Pencil

  8. Segment Addition Postulate: Thus, XY + YZ = XZ Segment Addition Postulate

  9. Maps The cities shown on the map lie approximately in a straight line. Use the given distances to find the distance from Lubbock, Texas, to St. Louis, Missouri. The distance from Lubbock to St. Louis is about 740 miles. ANSWER EXAMPLE 1 Apply the the Segment Addition Postulate SOLUTION Because Tulsa, Oklahoma, lies between Lubbock and St. Louis, you can apply the Segment Addition Postulate. LS = LT + TS = 380 + 360 = 740

  10. In the diagram, WY = 30. Can you use the Segment Addition Postulate to find the distance between points Wand Z? 4. ANSWER NO; Because w is not between x and z. for Examples 1 and 2 GUIDED PRACTICE

  11. 1. Use the Segment Addition Postulate to find XZ. ANSWER xz = 73 GUIDED PRACTICE SOLUTION xz = xy + yz Segment addition postulate = 23 + 50 Substitute 23 for xy and 50 for yz = 73 Add

  12. Use the diagram to find GH. FH = FG+ GH 36 21+GH = 15 GH = EXAMPLE 2 Find a length SOLUTION Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. Segment Addition Postulate. Substitute 36 for FHand 21 for FG. Subtract 21 from each side.

  13. 5. Use the diagram at the right to find WX. 144 = 37 + wx = wx 107 ANSWER WX = 107 GUIDED PRACTICE Use the segment addition postulate to write an equation. Then solve the equation to find WX SOLUTION vx = vw + wx Segment addition postulate Substitute 37 for vw and144for vx Subtract 37 from each side

  14. Example 3 Point S is between point R and point T. Use the given information to write an equation in terms of x. Solve the equation. Then find both RS and ST. RS = 3x – 16 ST = 4x – 8 RT = 60 I---------------60 -------------------I 3x-16 I-----------4x-8-----------I

  15. WARM-UP Directions: Find x. What do you notice about the relationship between segment AB and segment BC?

  16. 1.3 Lesson Use Midpoint and Distance Formulas

  17. Midpoint The midpoint of a segment is a point that divides a segment into 2 congruent segments. I I A B M So….. AM = MB

  18. Segment Bisector A point, segment, line, or plane that divides a line segment into two equal parts I I I I I I

  19. Skateboard In the skateboard design, VWbisects XYat point T, and XT=39.9cm. Find XY. Point Tis the midpoint of XY . So, XT = TY = 39.9 cm. Bisect: to cut in 1/2 EXAMPLE 1 Find segment lengths SOLUTION XY = XT + TY Segment Addition Postulate = 39.9 + 39.9 Substitute. = 79.8cm Add.

  20. ALGEBRA Point Mis the midpoint of VW. Find the length of VM . EXAMPLE 2 Use algebra with segment lengths

  21. GUIDED PRACTICE linel Identify the segment bisector of . Then find PQ.

  22. Warm Up: Find the coordinates of the midpoint

  23. MIDPOINT FORMULA The midpoint of two points P(x1, y1) and Q(x2, y2) is M(X,Y) = M(x1 + x2, y2 +y2) 2 2 Think of it as taking the average of the x’s and the average of the y’s to make a new point.

  24. a. FIND MIDPOINTThe endpoints ofRSare R(1,–3) and S(4, 2). Find the coordinates of the midpoint M. EXAMPLE 3 Use the Midpoint Formula

  25. 1 , – , M M = 2 5 2 The coordinates of the midpoint Mare 1 5 – , 2 2 ANSWER – 3 + 2 1 + 4 2 2 EXAMPLE 3 Use the Midpoint Formula SOLUTION a. FIND MIDPOINTUse the Midpoint Formula.

  26. FIND ENDPOINTLet (x, y) be the coordinates of endpoint K. Use the Midpoint Formula. b. FIND ENDPOINTThe midpoint of JKis M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K. STEP 1 Find x. STEP 2 Find y. 4+ y 1+ x 1 2 = = 2 2 ANSWER The coordinates of endpoint Kare (3, – 2). EXAMPLE 3 Use the Midpoint Formula 4 + y = 2 1 + x = 4 y =–2 x =3

  27. Guided Practice A. The endpoints of are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M. B. The midpoint of is M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V.

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