As Piaget highlighted, our brains make connections between new information and previous information (prior knowledge). I introduce the concept of congruent triangles by connecting it to prior knowledge of identical twins (photo above).
This connection is carried throughout the chapter. For example, to show triangles are congruent we look at parts of the triangle, just as we can look at shoe size, pants size and height of 2 people to determine if they are twins (see photo below).
Making math meaningful and maybe interesting is a challenge. The photo above refers to a real life application for triangles and trigonometry (see photo below) that is found in a news story about Russian jets and a US destroyer. The jet was flying at an altitude of 100 yards and within 200 yards of the destroyer. Topics that could be addressed:
Altitude (and perpendicular)
Trigonometry: e.g. find angle of elevation or depression
Vectors (include velocities)
A relevant, real life application is a method to make information meaningful. When talking about the altitude of a triangle (the up and down part shown in the photo below) the vocabulary term of altitude becomes more meaningful both in terms of context and with the visual below.
Here is the agenda I would follow to use this application as an activity.
I would show the video (show on the webpage linked at bottom of handout) and explain what a destroyer and the jets are.
Discuss the situation with Russia (age appropriate discussion)
Show the picture and ask the students to draw a sketch.
Review the sketch and refer to the parts of the triangle in real life terms, e.g. altitude.
Task the students with a problem related to this problem – create your own, e.g. find the angle of elevation or use Pythagorean Theorem to find length of missing side.