For ΔABC, ∠A = 4x - 4, ∠B = 6x - 1, and ∠C = 8x - 13. If ΔABC undergoes a dilation by a scale factor of 2 to create ΔA'B'C' with ∠A' = 51 - x, ∠B' = 4x + 21, and ∠C' = 6x + 9, which confirms that ΔABC∼ΔA'B'C by the AA criterion?
Accepted Solution
A:
Solution:As, Triangle ABC and Triangle A'B'C' will be similar to each other.So,their corresponding interior angles will be equal.So, ∠A=∠A'∠B=∠B'∠C=∠C'1. 4 x -4=51-x4x +x=51+45 x=55Dividing both sides by 11x=112. 6 x-1= 4 x +216x-4x=21+12x=22Dividing both sides by 2, givesx=11So, when x=11,the two triangles ΔABC∼ΔA'B'C by the AA criterion.