Question

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√2 cm
xz = 2(xy)
yz is the longest segment in △xyz.

Explanation:

Step1: Identify the type of triangle

Since $\angle X = 45^{\circ}$ and $\angle Z=45^{\circ}$ and $\angle Y = 90^{\circ}$, $\triangle XYZ$ is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the legs are equal. So, if \(XY = 9\mathrm{cm}\), then \(YZ=XY = 9\mathrm{cm}\) (because legs of a \(45 - 45-90\) triangle are congruent).

Step2: Use the Pythagorean theorem

For a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a = XY = 9\), \(b = YZ = 9\) and \(c=XZ\). Substitute into the formula:

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Also, in a right - triangle, the hypotenuse (\(XZ\)) is the longest side.

Answer:

• \(YZ = 9\mathrm{cm}\)
• \(XZ=9\sqrt{2}\mathrm{cm}\)