Question

use the graph to complete the statement to prove that \\( \triangle mno \\) is not congruent to \\( \triangle pqr \\).

segment qr cannot be mapped to by any composition of rigid motions.

review progress

Explanation:

Step1: Calculate the length of segment QR

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(Q(3,6)\) and \(R(3,2)\), we have \(QR=\sqrt{(3 - 3)^2+(6 - 2)^2}=\sqrt{0 + 16}=4\).

Step2: Calculate the length of segment NO

For \(N(-5,1)\) and \(O(-5,4)\), \(NO=\sqrt{(-5+5)^2+(4 - 1)^2}=\sqrt{0+9}=3\).

Step3: Calculate the length of segment MN

For \(M(-1,7)\) and \(N(-5,1)\), \(MN=\sqrt{(-1 + 5)^2+(7 - 1)^2}=\sqrt{16 + 36}=\sqrt{52}=2\sqrt{13}\).

Step4: Calculate the length of segment MO

For \(M(-1,7)\) and \(O(-5,4)\), \(MO=\sqrt{(-1+5)^2+(7 - 4)^2}=\sqrt{16 + 9}=5\).

Since \(QR = 4\), and among \(NO = 3\), \(MN=2\sqrt{13}\), \(MO = 5\), only \(NO\) has a different length from \(QR\).

Answer:

segment NO