Question

Determine whether each pair of segments is congruent

Answer 1

Set XY = XZ and solve for x
3x+5 = 5x-1
6=2x
x = 3
Then XY = 14 and XZ = 14 and YZ = 13.5
XY congruent XZ

Answer 2

Each pair of segments is not congruent, only XY and XZ segments is congruent.

Explanation:

Two figures are said to be congruent if both figures have the same shape, same dimension, they both appear the same and they both have the same angle measurement.

Thus, two segments are said to be congruent if they have same measurement.

Also, it is given in figure that,

XY = XZ

⇒ 3x + 5 = 5x - 1

⇒ 2x = 6

⇒ x = 3

Thus, XY = 3x + 5 = 3 × 3 + 5 = 14

XZ = 5x - 1 = 5 × 3 - 1 = 14

and, YZ = 9x ÷ 2 = (9 × 3 )÷ 2 = 13.5

Hence, Each pair of segments is not congruent, only XY and XZ segments is congruent.