Question

ethan created three triangles: triangle x, triangle y, and triangle z. if △y ≅ △x and △y ≅ △z. which must also be true?
triangles x, y, and z share one or more vertices.
the triangles are right triangles.
the triangles are equilateral.
triangles x and z are congruent.

Explanation:

Step1: Use the transitive property of congruence

If \( \triangle Y\cong\triangle X\) and \( \triangle Y\cong\triangle Z\), then by the transitive property of congruence (if \(a = b\) and \(a = c\), then \(b = c\) for congruent triangles), we can say something about \( \triangle X\) and \( \triangle Z\).

Step2: Apply the property to triangles

For congruent triangles, if \( \triangle Y\cong\triangle X\) (which means all corresponding sides and angles of \(Y\) and \(X\) are equal) and \( \triangle Y\cong\triangle Z\) (all corresponding sides and angles of \(Y\) and \(Z\) are equal), then all corresponding sides and angles of \(X\) and \(Z\) must be equal. So, \( \triangle X\cong\triangle Z\).

Answer:

Triangles \(X\) and \(Z\) are congruent.