If a series of rigid transformations maps ∠E onto ∠B where ∠E is congruent to ∠B, then which of the following statements is true? triangles ABC and FDE, in which angles A and D are right angles

ΔABC ~ ΔFDE because of the definition of similarity in terms of similarity transformations
segment DE ~ segment AB because corresponding parts of similar triangles are proportional
ΔABC ~ ΔFDE because of the AA similarity postulate
segment DE ~ segment AB because of the definition of similarity in terms of similarity transformations

C. ΔABC ~ ΔFDE because of the AA similarity postulate

Step-by-step explanation:

In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.

If two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.

so option C is your answer

hope it helps

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x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752