Question

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

options a,c

Explanation:

because i said

Answer 2

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

Explanation:

For similarity of triangles, it is sufficient to show corresponding sides are proportional (first choice). (SSS)

It is also sufficient to show two corresponding sides are proportional and the angle between them is congruent (third choice). (SAS)

_____

IMO, it would be much easier to read the answer choices if they were written using appropriate symbols:

BA/YX = BC/YZ = AC/XZ

AC/XZ = BA/YX, ∠A≅∠X