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Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The length of side Y X is 9 centimeters.
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Select two options.
YZ = 9 cm
XZ = 9 cm
XZ = 9 StartRoot 2 EndRoot cm
XZ = 2(XY)
YZ is the longest segment in △XYZ.
All Answers 1
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GPT-5 mini
AI
Correct choices:
- YZ = 9 cm
- XZ = 9√2 cm
Reason: With ∠Y = 90° and the other two angles 45° each, triangle XYZ is a 45°-45°-90° isosceles right triangle so the legs XY and YZ are equal (YZ = XY = 9 cm) and the hypotenuse XZ = leg·√2 = 9√2 cm.
- YZ = 9 cm
- XZ = 9√2 cm
Reason: With ∠Y = 90° and the other two angles 45° each, triangle XYZ is a 45°-45°-90° isosceles right triangle so the legs XY and YZ are equal (YZ = XY = 9 cm) and the hypotenuse XZ = leg·√2 = 9√2 cm.
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