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What is a similar figure?
What is the concept of similarity?
What is exact similitude in a metric space?
Does similar imply size?
A similarity (also called a similarity transformation or similitude) of a Euclidean space is a bijection f from the space onto itself that multiplies all distances by the same positive real number r, so that for any two points x and y we have ((), ()) = (,), where d(x,y) is the Euclidean distance from x to y.
- Definitions of similarity. Similar shapes & transformations. Practice. Similarity & transformations. 4 questions.
- Introduction to triangle similarity. Intro to triangle similarity. Triangle similarity postulates/criteria. (Opens a modal) Determining similar triangles.
- Solving similar triangles. Solving similar triangles: same side plays different roles. (Opens a modal) Practice.
- Angle bisector theorem. Intro to angle bisector theorem. Using the angle bisector theorem. (Opens a modal) Practice. Solve triangles: angle bisector theorem.
1. a. : counterpart, double. b. : a visible likeness : image. 2. : an imaginative comparison : simile. 3. a. : correspondence in kind or quality. b. : a point of comparison. Synonyms. alikeness. community. comparability. correspondence. likeness. parallelism. resemblance.
Similar figures are figures that are the same shape, but not necessarily the same size. Two figures are similar if and only if one figure can be obtained from the other by a single transformation , or a sequence of transformations, including translations, reflections, rotations and/or dilations.
Similar figures are two figures (or shapes) that have the same angles and proportional dimensions. In this lesson we look at how to find the similarity ratio (or similitude), and using that to determine the lengths of the side a of similar polygons, and how to find the height of a tree from its shadow. Introduction to Similar Figures. Watch on.
- 1 min
Similar figures are figures that are the same shape, but not necessarily the same size. We saw, when working with congruent triangles, that it was not necessary to show all six characteristics of congruent triangles to verify that the triangles were actually congruent. A similar idea applies to similar triangles. AA.
Intro to triangle similarity. Triangle similarity postulates/criteria. Angle-angle triangle similarity criterion. Determining similar triangles. Triangle similarity review. Practice. Determine similar triangles: Angles. Determine similar triangles: SSS. Prove triangle similarity. Quiz 1.
