Question

the graph shows quadrilaterals cdef and lmno. is cdef similar to lmno? justify your answer. yes, because a translation left 7 units and down 10 units maps cdef onto lmno. yes, because a rotation 180° around the origin maps cdef onto lmno. no, because ∠c and ∠l do not have the same measure.

Explanation:

Step1: Check the properties of translation

Translation is a rigid transformation. If a translation maps \(CDEF\) onto \(LMNO\), \(CDEF\) and \(LMNO\) would be congruent. But similarity requires a proportional scaling (if not congruent). Also, check the coordinates: assume \(C(4,9)\), if we translate left 7 units \(x = 4-7=-3\), down 10 units \(y=9 - 10=-1\). But \(L(-3,-9)\) (assuming coordinates from the graph - if \(C(4,9)\) and \(L(-3,-9)\) the translation rule is wrong.

Step2: Check the properties of rotation

Rotation of \(180^{\circ}\) around the origin has the rule \((x,y)\to(-x,-y)\). If \(C(4,9)\to(-4,-9)\) (not \(L(-3,-9)\)), so rotation \(180^{\circ}\) around the origin does not map \(CDEF\) onto \(LMNO\)

Step3: Consider the angle - angle similarity criterion

For two polygons to be similar, their corresponding angles must be equal. If \(\angle C\) and \(\angle L\) do not have the same measure (by visual inspection or using slope - angle relationship: slope of sides adjacent to \(\angle C\) and \(\angle L\) are different. For example, if we calculate the slopes of the sides of the quadrilaterals using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). The shape and angle - measures of \(CDEF\) and \(LMNO\) are not consistent with similarity (similar polygons have equal - angle measures)

Answer:

No, because \(\angle C\) and \(\angle L\) do not have the same measure.