which statement proves that △xyz is an isosceles right triangle?\n○ xz is not perpendicular to xy\n○…

which statement proves that △xyz is an isosceles right triangle?\n○ xz is not perpendicular to xy\n○ xz≠xy\n○ the slope of xz is $\frac{3}{4}$, the slope of xy is $-\frac{4}{3}$, and xz = xy = 5.\n○ the slope of xz is $\frac{3}{4}$, the slope of xy is $-\frac{4}{3}$, and the slope of zy = 7.

which statement proves that △xyz is an isosceles right triangle?\n○ xz is not perpendicular to xy\n○ xz≠xy\n○ the slope of xz is $\frac{3}{4}$, the slope of xy is $-\frac{4}{3}$, and xz = xy = 5.\n○ the slope of xz is $\frac{3}{4}$, the slope of xy is $-\frac{4}{3}$, and the slope of zy = 7.

Answer

Explanation:

Step1: Recall properties of isosceles right - triangle

An isosceles right - triangle has two equal sides and two perpendicular sides. The product of the slopes of two perpendicular lines is - 1.

Step2: Check slope condition

If the slope of $\overline{XZ}$ is $\frac{3}{4}$ and the slope of $\overline{XY}$ is $-\frac{4}{3}$, then the product of their slopes is $\frac{3}{4}\times(-\frac{4}{3})=- 1$, so $\overline{XZ}\perp\overline{XY}$.

Step3: Check side - length condition

We need to check if two sides are equal. If $XZ = XY=5$, then two sides are equal.

Answer:

C. The slope of $\overline{XZ}$ is $\frac{3}{4}$, the slope of $\overline{XY}$ is $-\frac{4}{3}$, and $XZ = XY = 5$.