320,667 views
45 votes
45 votes
which of the following statements is correct?A XYZ ~ wvz by AA similarityB XYZ ~ WVZ by SAS similarityC XYZ ~ WVZ by SSS similarityD XYZ and WVZ are not similar

which of the following statements is correct?A XYZ ~ wvz by AA similarityB XYZ ~ WVZ-example-1
User David Essien
by
2.7k points

1 Answer

19 votes
19 votes

We have two triangles, XYZ and WVZ.

They shared the vertex Z, formed by the intersection of two lines, XW and VY.

Also, XY and VW are parallel.

Then, we have a pair of congruent angles at vertex Z, as they are vertical angles.

We also have another pair of congruent angles: V and Y, because they are alternate interior angles between parallel lines.

Then, as we have two pair of congruent angles, the third pair of angles have to be congruent too, as the measures of the interior angles of a triangle always add 180°.

Then, if we have 3 pair of congruent angles, we have similar triangles.

We can not say anything about congruent sides because we don't know any relation or proportion between them, so the other postulates, SAS or SSS, can not be used.

Answer: XYZ ~ WVZ by AA similarity (Option A)

User Ludovico Fischer
by
2.9k points