Section 16.2: Proving Figures are Similar Using Transformations

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Presentation transcript:

Section 16.2: Proving Figures are Similar Using Transformations

Objective: By following instructions, students will be able to: Explain how similarity transformations can be used to show two figures are similar.

A similarity transformation is a transformation in which an image has the same shape as its pre-image. Similarity transformations can include: 1. Reflections 2. Rotations 3. Translations 4. Dilations

Reflection (Flip)

Translation (Slide) 5

Rotation (Turn) 6

Dilation 7

You can represent dilations using the coordinate notation (x,y)(kx, ky) where k is a scale factor and the center of dilation is the origin. If 0<k<1, the dilation is a reduction. If k>1, the dilation is an enlargement.

explain 1A Determine whether the two figures are similar using similarity transformations. Explain.

explain 1B Determine whether the two figures are similar using similarity transformations. Explain.

Your-Turn #1 Determine whether the two figures are similar using similarity transformations. Explain. LMNO and GHJK

explain 2A Find a sequence of similarity transformations that maps the first figure to the second figure. Write the coordinate notation for each transformation. ABDC to EFHG

explain 2B Find a sequence of similarity transformations that maps the first figure to the second figure. Write the coordinate notation for each transformation. triangle JKL to triangle PQR

Your-Turn #2 Find a sequence of similarity transformations that maps the first figure to the second figure. Write the coordinate notation for each transformation.

Revisit Objective: Did we… Explain how similarity transformations can be used to show two figures are similar?

HW: Sec 16.2 page 644 #s 1-10, 18-20