Question

AB || CD || EF and AC = CE. Find x if

1. BD = 3x + 2 and DF = 4x – 3
2. BD = 5x – 4 and BF = 4x + 16

Answer 1

Step 1:

Apply the Intercept Theorem

Since AB || CD || EF and AC = CE, it implies that BD = DF

Step 2: 

Solve for x in case (i)

Set BD = DF: 3x + 2 = 4x – 3

Subtract 3x from both sides: 2 = x – 3

Add 3 to both sides: x = 5

Step 3:

Solve for x in case (ii)

Use the segment addition postulate: BF = BD + DF

Since BD = DF, substitute DF with BD: BF = BD + BD = 2BD

Substitute the given expressions: 4x + 16 = 2(5x – 4)

Distribute the 2: 4x + 16 = 10x – 8

Subtract 4x from both sides: 16 = 6x – 8

Add 8 to both sides: 24 = 6x

Divide by 6: x = `24/6` = 4

The value of x is 5 for the first case and 4 for the second case.