Question

Which statements are true regarding the sides and angles of the triangle? Select three options. Line segment X Y is the longest side. Angle X is the largest angle. Angle Z is greater than angle Y. Line segment X Z is opposite the largest angle. Line segment X Z is the shortest side.

Answer 1

bce

Explanation:

Answer 2

B. Angle X is the largest angle.

C. Angle Z is greater than angle Y.

E. Line segment X Z is the shortest side.

Explanation:

YZ = 2n, XZ = n - 2, XY = n + 4 and n ≥ 5.

YZ - XZ = 2n - (n - 2) = n + 2. but n ≥ 5, hence YZ - XZ = n + 2 ≥ 7.

YZ > XZ

YZ - XY = 2n - (n + 4) = n - 4. but n ≥ 5, hence YZ - XY = n - 4 ≥ 1

YZ > XY

XY - XZ = n + 4 - (n - 2) = 6: XY > XZ

Therefore:

YZ > XY > XZ

The angles are proportional to their opposite sides, hence:

∠X > ∠Z > ∠Y

A. Line segment XY is the longest side.

This is wrong because YZ is the longest side.

B. Angle X is the largest angle.

This is correct. ∠X is the largest angle because it is opposite to the longest side (YZ)

C. Angle Z is greater than angle Y.

This is correct. ∠Z is opposite to the side XY while ∠Y is opposite to the side XZ

D. Line segment XZ is opposite the largest angle.

This is wrong. ∠X is the largest angle which is opposite to the longest side (YZ)

E. Line segment X Z is the shortest side.

This is correct