Question

In Triangle XYZ, XZ = YZ and mZ = 74°. The longest side of the triangle is...
A. XZ
B. YZ
C. XY
D. Xm

Answer 1

@amistre64

Answer 2

@ivettef365

Answer 3

Since XZ and YZ are congruent, you can assume that this is an isosceles triangle. Now the angle corresponding to the two congruent sides is 74 degrees, and since the two sides adjacent to it are congruent, the degree of the other two angles is the same.
Let's find the other two angles:
180=74+2x (I put 2 x because we understand the other two angles are congruent.)
106 = 2x
53=x
So now we know that the three angles are 53, 53, and 74. The longest side of any triangle can be found by finding the largest angle then moving to the only side not touching said angle. Since mZ is the largest at 74 degrees, then XY must be the longest side. Does this make sense?

Answer 4

yes thank you