Question

the graph shows quadrilaterals fghi and lmno. is fghi congruent to lmno? justify your answer. yes, because a translation right 12 units maps fghi onto lmno. yes, because a reflection across the y - axis maps fghi onto lmno. no, because \\( \overline { fg } \\) and \\( \overline { lm } \\) do not have the same length. no, because \\( \angle h \\) and \\( \angle n \\) do not have the same measure.

Explanation:

Step1: Calculate the length of \( \overline{FG} \)

Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For \( F(-8,8) \) and \( G(-7,5) \), \( d_{FG}=\sqrt{(-7+8)^2+(5 - 8)^2}=\sqrt{1 + 9}=\sqrt{10} \)

Step2: Calculate the length of \( \overline{LM} \)

For \( L(8,6) \) and \( M(7,4) \), \( d_{LM}=\sqrt{(7 - 8)^2+(4 - 6)^2}=\sqrt{1+4}=\sqrt{5} \)

Step3: Compare the lengths

Since \( \sqrt{10}
eq\sqrt{5} \), \( \overline{FG} \) and \( \overline{LM} \) are not equal. Congruent polygons have all corresponding sides equal.

Answer:

No, because \( \overline{FG} \) and \( \overline{LM} \) do not have the same length.