5 What is Similarity
1 Early Concept of Like or Similar Shapes
2 Similarity By Design
3 Similarity by Design with coordinates
4 Similarity - Definition with Coordinate
5 Similarity of Circles Squares and Rectangles
6 Geometric Diagrams in Class
7 Translations Rotations Reflections Dilatations
8 Similarity of Triangles and Polygons
9 Similarity of Triangles Usual Criteria
10 Similarity of Triangles - Equivalent of Two Criteria
11 Triangle Similarity Missing Side Problem
12 Triangles Similarity More Problems
13 Navigation Location from Angles to 2 Landmarks
This folder What is Similarity provides a general and unified treatment of
the likeness or similarity of squares, circles, triangles and
arbitary regions in the plane. The lessons here can be covered after
section 1 on maps, plans and measurement and after the introduction
of Cartesian coordinates. The objective here is to explain and
reconcile different characterizations of similarity.
The key question is how to recognized similarity. In modern life,
objects are similar by design if they stem from the same plans but
are built to different scales. That reflects a coordinate view point
of similarity objects. Two objects are similar if we can attach
coordinate system to each so that the set of coordinates for the
points for one object essentially provides the plan for the other as
is or after the application of a scale factor - a dilatation. This
set of coordinate development easily explains how and why circles,
squares and rectangles - those with a common aspect ratio - may be
similar. The coordinate perspective of similarity in the case of
similar triangles and more generally in the case of similar polygons
implies corresponding angles are equal and corresponding sides are
proportional. A partial proof of the converse is included in the
section what is similarity - a full proof is left to later as site
development to do.
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