I'm having trouble with a proof; I have to explain why angles are congruent in a dilation. Thanks.

Given: ∠A ≅ ∠X and ∠B ≅ ∠Y
Prove: ΔABC ~ ΔXYZ

A) Apply a dilation to ΔABC with scale factor . Let the image of ΔABC be ΔA′B′C′.

∠A′ ≅ ∠A and ∠B′ ≅ ∠B because: ?

Question

I'm having trouble with a proof; I have to explain why angles are congruent in a dilation. Thanks.

Given: ∠A ≅ ∠X and ∠B ≅ ∠Y
Prove: ΔABC ~ ΔXYZ

  A)   Apply a dilation to ΔABC with scale factor  . Let the image of ΔABC be ΔA′B′C′.
 
∠A′ ≅ ∠A   and ∠B′ ≅ ∠B because: ?

anonymous · Answer

attachment

ganeshie8 · Answer

You may put ur argument something like below :
In dilation, the lines get scaled by some factor $ k$, and each point $(x, y)$ maps to a new point $(kx, ky)$. Since all the points are getting shifted by the same amount, the lines in the dilated image will be parallel to the preimage. Hence the angle measures will not change under dilation. @dan815 may like to correct/add more :)

nincompoop · Answer

dilation and constriction are just a proportionality of the original shape

dan815 · Answer

first part is straight forward, by AAA property they are similar
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2nd part to show that these angles are equal
we can work with 3 vectors |dw:1405227605545:dw|