Question

answer attempt 1 out of 2
figure hijk congruent to figure mnop because rigid motions
used to map figure hijk onto figure mnop.
figure hijk similar to figure mnop because rigid motions and/or dilations
be used to map figure hijk onto figure mnop.

Explanation:

Step1: Understand Congruence and Similarity

Congruent figures have the same shape and size. Rigid motions (translations, rotations, reflections) preserve shape and size. Similar figures have the same shape but different sizes. They may involve rigid motions and dilations (scaling).

Step2: Analyze the Figures

Looking at the coordinates of the vertices of \(HIJK\) and \(MNOP\), if we can map \(HIJK\) onto \(MNOP\) using only rigid motions (no dilation), then they are congruent. If a dilation (in addition to rigid motions) is needed, they are similar.
Assume we check the side - lengths. For example, calculate the length of \(HI\) and \(MN\) using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Let \(H(x_1,y_1)\), \(I(x_2,y_2)\), \(M(x_3,y_3)\), \(N(x_4,y_4)\).
The distance formula: \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). If the side - lengths of \(HIJK\) and \(MNOP\) are equal (after applying rigid motions like translation, rotation, reflection), then they are congruent.

Answer:

Figure \(HIJK\) is congruent to Figure \(MNOP\) because rigid motions can be used to map Figure \(HIJK\) onto Figure \(MNOP\).