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Two figures are congruent if the second figure can be obtained from the first figure by a sequence of rotations, reflections, and translations.
Look for a sequence of transformations that will map △ DEF onto △ D'E'F'.
B
Yes, see solution.
To decide, let's recall an important property.
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Two figures are congruent if the second figure can be obtained from the first figure by a sequence of rotations, reflections, and translations. |
The property tells us that we need to look for a sequence of transformations that will map △ DEF onto △ D'E'F'. This is the way described in option B. Note that using only one type of transformation may not be enough. This is why all the other answers are incorrect.
We want to decide if triangles DEF and D'E'F are congruent.
Based on what we said in Part A, we need to look for a sequence of transformations that will map △ DEF onto △ D'E'F'. Let's start with a translation. We will map the vertex F onto its corresponding vertex F'. This means translating the triangle DEF 4 units down and 1 unit left.
Looking at the graph, we can see that △ D'E'F' looks like a rotation of △ DEF. Let's rotate △ DEF about point F so that sides EF and E'F' align. If △ DEF maps onto △ D'E'F', then we will know for sure that the triangles are congruent. Let's do it!
We were able to map △ DEF onto △ D'E'F' after a translation and a rotation. The triangles are congruent since a sequence of transformations exists that maps △ DEF onto △ D'E'F'.
