[G.SRT.2] Similarity, Right Triangles, and Trigonometry #2

Objective

Common Core Text:

• [G.SRT.2] Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Said Differently:

• • Understand the meaning of similarity transformations

  • Explain the general meaning of similarity, especially for triangles

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Explanation

You already learned about a class of transformations called rigid motions

• • Rigid motions use

    1. Translation

    2. Rotation

    3. Reflection

  • Rigid motions create images whose corresponding angles and line segments are congruent

Similarity transformations are another class of transformations.

• • Similarity transformations use

    1. Translation

    2. Rotation

    3. Reflection

• 1. Dilation

• • Similarity transformations create images whose corresponding angles are congruent and whose corresponding line segments are proportional

Do you see the difference between rigid motions and similarity transformations?

• • Similarity transformations use rigid motions, and dilation

  • Both have congruent angles, but in similarity transformations, corresponding line segments only have to be proportional, not necessarily congruent. (This is because dilations create proportional lines)

Can you wrap your mind around this?

• • "All rigid motions are similiarity transformations, but only some similarity transformations are rigid motions."

    • Which similarity transformations are rigid motions? Ones with no dilation!

pictures of easy coordinate plane similarity transformations and non-sim trans, such as page 138 in OnCore.

Also perhaps some triangles where the sides and angles are just given, and they have to check for proportionality