Question

What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.

∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE

Answer 1

Answer: ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE are the additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

Explanation:

Given: ΔXYZ and ΔEFG such that ∠X=∠F

To prove they are congruent by using ASA or AAS conruency criteria

we need only one angle and side.

1. ∠Z ≅ ∠G(angle) and XZ ≅ FG(side)

so we can apply ASA such that ΔXYZ ≅ ΔFEG.

2. ∠Z ≅ ∠G (angle)and ∠Y ≅ ∠E (angle), we need one side which is not present here.∴we can not apply ASA such that ΔXYZ ≅ ΔFEG.

3. XZ ≅ FG (side) and ZY ≅ GE (side), we need one angle which is not present here.∴we can not apply ASA such that ΔXYZ ≅ ΔFEG.

4. XY ≅ EF(side) and ZY ≅ FG(side), not possible.

5. ∠Z ≅ ∠G(angle) and XY ≅ FE(side),so we can apply ASA such that

ΔXYZ ≅ ΔFEG.