Question

In this diagram, AT = 2x + 3, CT = 3x - 1, BT = x + 5,

DT = 4x + 1, and mLATD = 41x + 8. If x = 2,
which segment is the perpendicular bisector of the other? Explain your reasoning.

Answer 1

CT is the perpendicular bisector of AB

Explanation:

calculate the segments using x = 2

AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7

BT = x + 5 = 2 + 5 = 7

thus AT = BT

CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5

DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9

thus CT ≠ DT

∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°

Thus CT is the perpendicular bisector of AB