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

Answer: Answer is 3

BC        6

------ = ------

XY         3

Step-by-step explanation:

The statements below can be used to prove that the triangles are similar.

On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.  

A B Over X Y = 4 Over 2

?  

A C Over X Z = 52 Over 13  

△ABC ~ △XYZ by the SSS similarity theorem.

Which mathematical statement is missing?

1.   Y Z Over B C = 6 Over 3  

2.  ∠B ≅ ∠Y

3.  B C Over Y Z = 6 Over 3  

4.  ∠B ≅ ∠Z

Answer 2

Answer:

• 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

Step-by-step explanation:

Given the way the triangles are named, corresponding sides are ...

  (BA, YX), (BC, YZ), (AC, XZ)

and corresponding angles are ...

  (A, X), (B, Y), (C, Z).

Similarity can be shown by having all three sides proportional (SSS), or by having any two angles congruent (AA), or by having two proportional sides and the angle between them (SAS).

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The offered answer choices (in order) are ...

• SSS similarity (one of the answers)
• SSA similarity (not an option--except in a special case where more information is available)
• SAS similarity (one of the answers)
• non-corresponding sides proportional (nonsense)
• non-corresponding sides and non-corresponding angles (nonsense)