Question

Which of the following explains how Δaeb could be proven similar to Δdec using the aa similarity postulate?

1) ∠aeb ≅ ∠ced because vertical angles are congruent; reflect Δced across segment fg, then translate point d to point a to confirm ∠eab ≅ ∠edc.
2) ∠aeb ≅ ∠ced because vertical angles are congruent; rotate Δced 180° around point e, then dilate Δced to confirm segment eb ≅ segment ec.
3) ∠aeb ≅ ∠dec because vertical angles are congruent; rotate Δced 180° around point e, then translate point d to point a to confirm ∠eab ≅ ∠edc.
4) ∠aeb ≅ ∠dec because vertical angles are congruent; reflect Δced across segment fg, then dilate Δced to confirm segment eb ≅ segment ed.

Answer 1

To prove that Δaeb is similar to Δdec using the AA similarity postulate, option 3 is the correct explanation. It suggests rotating Δced 180° around point e and then translating point d to point a to confirm that the corresponding angles are congruent.

Step-by-step explanation:

To prove that Δaeb is similar to Δdec using the AA similarity postulate, we need to show that the corresponding angles of the two triangles are congruent.

1. Option 1 suggests reflecting Δced across segment fg and translating point d to point a to confirm that ∠eab is congruent to ∠edc. However, this does not prove that all corresponding angles of the two triangles are congruent, so it is not the correct explanation.
2. Option 2 suggests rotating Δced 180° around point e and dilating it to confirm that segment eb is congruent to segment ec. Again, this does not prove that all corresponding angles are congruent, so it is not the correct explanation.
3. Option 3 suggests rotating Δced 180° around point e and then translating point d to point a to confirm that ∠eab is congruent to ∠edc. This is the correct explanation according to the AA similarity postulate because it shows that the corresponding angles are congruent.
4. Option 4 suggests reflecting Δced across segment fg and then dilating it to confirm that segment eb is congruent to segment ed. This does not prove that all corresponding angles are congruent, so it is not the correct explanation.

Therefore, option 3 is the correct explanation for proving the similarity of Δaeb to Δdec using the AA similarity postulate.