<u>Answer-</u>
- YZ = 9 cm
- XZ is the longest segment in triangle XYZ.
<u>Solution-</u>
Triangle XYZ is a right angle triangle with ∠Y=90°
Triangle XYZ is also an isosceles triangle, as
∠X =45°= ∠Z
Therefore, triangle XYZ is a right angle isosceles triangle.
So,
XY = YZ = 9 cm
Applying Pythagoras theorem,
In a right angle triangle, always the hypotenuse is the largest. So XZ is the longest segment in triangle XYZ.