Answer:
- Think again
- Think again
Explanation:
The idea involved in showing similarity is that some angle-preserving transformation of one figure will cause it to be congruent to another figure. The transformations usually used are translation, dilation, and rotation.
A smaller figure needs to be dilated by a factor greater than 1 to make it congruent to a larger figure. Corresponding angles need to have their vertices match. With these thoughts in mind, consider the questions asked here.
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1. The names of the two figures tell you point P corresponds to point L, and point Q corresponds to point M. Any translation should involve overlaying the corresponding points, so all of the answer choices got that part right.
We observe that PQ is shorter than LM, so any dilation of PQRS needs to be by the factor LM/PQ to make it match the larger figure. Considering the above description of how we show similarity, we know we need to do both a translation and a dilation. The only viable answer choice is the first one:
Translate PQRS so point P lies on point L, then dilate PQRS by the ratio LM/PQ.
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2. From the above discussion, we know that dilating ΔABC by the factor AD/AB or the factor AE/AC will allow checking to see if AB'C' ≅ ADE. However, the two answer choices suggesting these dilations talk about similarity of line segments, when we're trying to show AA similarity.
Translating an angle to the location of its corresponding angle will show whether those angles are congruent, hence AA similarity. However that translation must match corresponding vertices. We're trying to show ΔABC ~ ΔADE, so the corresponding vertices are (B, D) and (C, E). Translating vertex B to the location of E does nothing useful. Rather, vertex C needs to be translated to the location of E so the angles ACB and AED can be compared.
Translate ΔABC so point C lies on point E to confirm ∠C ≅ ∠E.