∆ABC ~ ∆DEF . . . as markedEF/LM = FG/MN . . . look againSAS congruence . . . as marked30 ft
Step-by-step explanation:
1. Correct. Corresponding vertices are (A, D), (B, E), and (C, F). The triangle names must list corresponding vertices in the same order. Thus the answer is the one you have chosen.
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2. Look again. As in the first problem, corresponding vertices are in the same order. Line segment EF is named by the first two vertices in the triangle name, so the corresponding segment is LM, also named by the first two vertices of that triangle's name.
Segment FG is named by the last two vertices of the triangle's name, so the corresponding segment in the other triangle is also named by the last two vertices of the triangle's name: MN. Corresponding segments are proportional, so EF/LM = FG/MN.
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3. Correct. Segment DB is congruent to itself. The halves of the bisected angle at D are congruent to each other, and the segments DA and DC are shown as congruent. Hence, SAS is an appropriate choice for showing congruence of the triangles.
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4. The 1:1 ratio of these similar triangles tells you they are congruent, so ...
AC = EC
4x -3 = 2x +6 . . . . substitute the given expressions
2x = 9 . . . . . . . . . . add 3-2x
EC = 9+6 = 15 . . . substitute for 2x in the expression for EC
The question asks for AE, which is 2 times the length EC, so is ...
AE = 2·EC = 2·15 = 30 . . . . feet
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The only indication that the units are feet is that the answer choice with the number 30 has feet as its units. (We should be seeing "(4x-3) feet" as the measure of AC, for example.)
