Question

"AABC ~ ADEF. The two green triangles are similar. Which postulate proves this? Find the measure of side AB.

A) Side-Angle-Side (SAS) Postulate
B) Angle-Angle (AA) Postulate
C) Side-Side-Side (SSS) Postulate
D) Angle-Side-Angle (ASA) Postulate
E) The information provided is not sufficient to determine the postulate."

Answer 1

The two triangles are similar using the Angle-Angle (AA) Postulate. Side AB can be found using the properties of similar triangles and setting up a proportion.

Step-by-step explanation:

In this case, the two triangles AABC and ADEF are similar. To prove this, we can use the Angle-Angle (AA) Postulate. According to this postulate, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, we can observe that angle A is congruent to angle A, and angle B is congruent to angle D. Therefore, we can conclude that the two triangles are similar.

To find the measure of side AB, we can use the properties of similar triangles. Since the two triangles are similar, the corresponding sides are proportional. We can set up the following proportion:

AAB'C ~ ADEF ==> AB/AD = AB'/AD'.

We can substitute the given values into the proportion and solve for AB:

AB/10 = 12/8 ==> AB = (10 * 12) / 8 = 15.