Congruence vs. Similarity

Today, we learned about Congruence versus Similarity.

Objective:
Students will differentiate between congruent and similar triangles.

TEKS:
G.10.B
The student is expected to justify and apply triangle congruence
relationships.

G.11.C
The student is expected to develop, apply, and justify triangle similarity

relationships, such as right triangle ratios,
trigonometric ratios, and Pythagorean triples
using a variety of methods.

We learned that similar triangles have the same angle measures. Mr. Escalante said they have to have "corresponding angles" that are the same, which is just a fancy way of saying that each angle in one triangle has to equal an angle in the other triangle. You can use angle-angle (AA) to identify similar triangles. This works because if you know two angles, then you automatically know the third by the Angle Sum Theorem, which we already learned.

Congruent triangles have the same angle measures, but they also have the same side lengths.  Basically, a congruent triangle is a similar triangle where the sides of the first triangle are the same size as the sides of the second triangle. You can use side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA) to identify congruent triangles.

This lesson was kind of cool because it took the things we learned about angle sums, similarity and congruence and made them make sense. I liked how Mr. E. showed us a triangle then stretched it out without changing the angles to explain similarity.  I am still confused about why SSS is enough to make triangles congruent. Why can't the angles change when the sides are the same?

Question of the day:

House builders are working on a roof, and they want to figure out how far it will be from the peak of the roof to the bottom of the eaves.  They have a scale model of the house that is 10 inches wide from eaves to eaves. They also know that the house is 50 feet wide from eaves to eaves.  Will they use similarity or congruence to find the desired measurement? Do they have enough information to be confident? If not, what information do they need?