Question

Please describe some of these new postulates and include a diagram on the whiteboard to help explain how they are applied.You have learned some new ways in this module to prove that triangles are similar Please describe some of these new postulates and include a diagram on the whiteboard to help explain how they are applied.

Answer 1

The Solution:

Required:

To use the three theorems of similarity:

There are 3 theorems for proving triangle similarity:

AA Theorem

SAS Theorem

SSS Theorem

SAS Theorem

What happens if we only have side measurements, and the angle measures for each triangle are unknown? If we can show that all three sides of one triangle are proportional to the three sides of another triangle, then it follows logically that the angle measurements must also be the same.

SSS Theorem

Or what if we can demonstrate that two pairs of sides of one triangle are proportional to two pairs of sides of another triangle, and their included angles are congruent?

AA Theorem

As we saw with the AA similarity postulate, it’s not necessary for us to check every single angle and side in order to tell if two triangles are similar. Thanks to the triangle sum theorem, all we have to show is that two angles of one triangle are congruent to two angles of another triangle to show similar triangles.