BraceFaceZariaOn32
04.08.2019 •
Mathematics
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?
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Ответ:
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-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.
Ответ:
X = 60° (corresponding angles are equal )