Question

State whether the triangles are similar if so write a similarity statement and the postulate or theorem you used? Triangle one is 5,5,8 and triangle 2 is 7.5,7.5, and 12.

A) Similar, by SSS
B) Not similar
C) Similar, by AA
D) Similar, by SAS

Answer 1

The triangles are similar by the SSS similarity postulate because all corresponding sides of the two triangles are in the same proportion.

Step-by-step explanation:

To determine whether the two triangles are similar, we can use one of the similarity postulates or theorems such as the Side-Side-Side (SSS) similarity postulate, the Angle-Angle (AA) similarity theorem, or the Side-Angle-Side (SAS) similarity theorem. In our case, since all three corresponding sides of triangle one (5, 5, 8) and triangle two (7.5, 7.5, 12) are in the same proportion (5/7.5 = 2/3 and 8/12 = 2/3), we can conclude that the triangles are similar by the SSS similarity postulate.