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In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY .

Skateboard. In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY. Point T is the midpoint of XY . So , XT = TY = 39.9 cm. EXAMPLE 1. Find segment lengths. SOLUTION. XY = XT + TY. Segment Addition Postulate. = 39.9 + 39.9. Substitute. = 79.8 cm.

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In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY .

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  1. 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. EXAMPLE 1 Find segment lengths SOLUTION XY = XT + TY Segment Addition Postulate = 39.9 + 39.9 Substitute. = 79.8cm Add.

  2. ALGEBRA Point Mis the midpoint of VW. Find the length of VM . STEP 1 Write and solve an equation. Use the fact that that VM = MW. EXAMPLE 2 Use algebra with segment lengths SOLUTION VM= MW Write equation. 4x–1= 3x + 3 Substitute. x – 1 = 3 Subtract 3xfrom each side. x = 4 Add 1 to each side.

  3. STEP 2 Evaluate the expression for VMwhen x = 4. So, the length of VMis 15. Check: Because VM = MW, the length of MWshould be 15. If you evaluate the expression for MW, you should find that MW = 15. MW = 3x + 3 = 3(4) +3 = 15 EXAMPLE 2 Use algebra with segment lengths VM = 4x – 1 = 4(4) – 1 = 15

  4. M is midpoint and line MN bisects the line PQ at M. SoMNis the segment bisector of PQ. So PM = MQ =1 PQ = PM + MQ = 1 1 3 + 7 7 7 3 8 8 8 4 = for Examples 1 and 2 GUIDED PRACTICE In Exercises 1 and 2, identify the segment bisectorof PQ . Then find PQ. 1. SOLUTION Segment addition postulate. Substitute Add.

  5. In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. for Examples 1 and 2 GUIDED PRACTICE 2. SOLUTION M is midpoint and line l bisects the line PQ of M. So lis the segment bisector of PQ. So PM = MQ

  6. STEP 1 Write and solve an equation Evaluate the expression for PQwhen x = + 4 x = 18 7 STEP 2 3 5 11 7 18 Substitute for x. 7 18 18 PQ = 7 7 = for Examples 1 and 2 GUIDED PRACTICE PM = MQ Write equation. 5x – 7 = 11–2x Substitute. 7x = 18 Add 2xand 7 each side. Divide each side by 7. PQ = 5x – 7 + 11 – 2x = 3x + 4 Simplify.

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