Question

Triangles A B C and X Y Z are shown.
Which would prove that ΔABC ~ ΔXYZ? Select two options.

StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction = StartFraction A C Over X Z EndFraction
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction , angle C is-congruent-to angle Z
StartFraction A C Over X Z EndFraction = StartFraction B A Over Y X EndFraction , Angle A is-congruent-to Angle X
StartFraction B A Over Y X EndFraction = StartFraction A C Over Y Z EndFraction = StartFraction B C Over X Z EndFraction
StartFraction B C Over X Y EndFraction = StartFraction B A Over Z X EndFraction , Angle C is-congruent-to angle X.

Answer 1

Choose the first and the third options.

- First: BA/YX = BC/YZ = AC/XZ — gives SSS similarity.
- Third: AC/XZ = BA/YX , ∠A ≅ ∠X — gives SAS similarity (the equal angle is included between the two proportional sides).