Question

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?

Answer 1

B) C) E) IS THE ANSWER

Explanation:

Answer 2

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-x

4x +x=51+4

5 x=55

Dividing both sides by 11

x=11

2. 6 x-1= 4 x +21

6x-4x=21+1

2x=22

Dividing both sides by 2, gives

x=11

So, when x=11,the two triangles ΔABC∼ΔA'B'C by the AA criterion.