EXAMPLE 1 Find segment lengths Skateboard In the

EXAMPLE 1 Find segment lengths Skateboard In the skateboard design, VW bisects XY at point T, and XT = 39. 9 cm. Find XY. SOLUTION Point T is the midpoint of XY. So, XT = TY = 39. 9 cm. XY = XT + TY Segment Addition Postulate = 39. 9 + 39. 9 Substitute. Add. = 79. 8 cm

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

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

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

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

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