Note: Your teacher will grade your responses to the following question to ensure you receive proper credit for your answers.
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. The diagram is not drawn to scale.
Triangle JKO is shown inside of triangle MNO. Side OJ = 30, JM = 10, OK = 3 and KN = 1.
To determine whether the triangles JKO and MNO are similar, we need to compare their corresponding sides.
For the sides OJ and NO, we cannot compare them directly because they are not corresponding sides.
However, we can compare the ratios of the corresponding sides JM and MN, and OK and ON, to see if they are equal.
The ratio of JM to MN is 10:1, and the ratio of OK to ON is 3:1.
Since the ratios of the corresponding sides are equal (10:1 = 3:1), we can conclude that the triangles JKO and MNO are similar.
The similarity statement is: Triangle JKO is similar to triangle MNO.
The postulate or theorem used is the Angle-Angle (AA) similarity postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.