Question

which of the following sets of ordered pairs will produce a triangle with vertices x, y, and z that is congruent to △prt? z(0, 2) z(5, 2) z(6, 2) z(5, 3)

Explanation:

Step1: Recall congruent - triangle properties

Two triangles are congruent if they have the same shape and size, which means corresponding sides and angles are equal. In a coordinate - plane, we can use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find side lengths. However, we can also use visual inspection and the fact that for congruent right - triangles, we can match side lengths and orientations. Since no coordinates of $\triangle PRT$ are given precisely, assume we are looking at a right - triangle with a vertical and a horizontal side. Given $X$ and $Y$ positions, we need to find a $Z$ such that the triangle formed has the same side - length relationships as $\triangle PRT$.

Step2: Analyze the options

If we assume that the triangle formed by $X$, $Y$, and $Z$ should have a right - angle and appropriate side lengths to match $\triangle PRT$. If $X$ and $Y$ are on a vertical and horizontal line respectively, for a right - triangle, we need to complete the right - triangle. If we assume the horizontal distance between $X$ and $Y$ is a certain value, and we want to form a right - triangle similar in shape to $\triangle PRT$. Looking at the options, if we consider the right - triangle formed by the points, for a right - triangle with vertices $X$ and $Y$ where $X$ is above $Y$ on a vertical line, we need a $Z$ such that the side lengths match. If we assume the horizontal and vertical side lengths of $\triangle PRT$ and try to replicate them with $X$, $Y$, and $Z$. The most likely option is when the triangle has the correct orientation and side - length relationships. If we assume that the horizontal distance and vertical distance between the vertices of $\triangle PRT$ are replicated in the triangle with vertices $X$, $Y$, and $Z$. Given the vertical line through $X$ and horizontal line through $Y$, to form a right - triangle, if we assume the side - length relationships, the point $Z(5,2)$ will form a right - triangle with $X$ and $Y$ that is likely to be congruent to $\triangle PRT$.

Answer:

Z(5, 2)