Determine whether each pair of segments is congruent

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

Step-by-step 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.

This value is approximate.

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Explanation:

To find the perimeter, we simply add up the lengths of the three external sides.

The horizontal side from D to E is 16 units long since |-10-6| = 16. I subtracted the x coordinates of the points and applied absolute value. You could also count out the spaces and you should count 16 spaces from D to E.

Unfortunately, the diagonal lengths aren't as straight forward. We have two options here: The pythagorean theorem, or the distance formula.

I'll go with the distance formula.

Let's find the distance from C to D, aka the length of side CD

Side CD is roughly 9.2195 units long.

Repeat this idea to find the length of CE

Side CE is roughly 7.2801 units long

The perimeter of triangle CDE is approximately...

P = DE+CD+CE

P = 16 + 9.2195 + 7.2801

P = 32.4996

This then rounds to 32.5 units. The answer is choice C.