Prove two figures are similar after a dilation

Prove two figures are similar after a dilation

In this lesson you will learn how to determine if two figures are similar by using dilations and scale factors.

ADDITIONAL MATERIALS

STANDARDS

CCSS.8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

TEKS.8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane;

TEKS.8.10.C explain the effect of translations, reflections over the 𝑥- or 𝑦-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and

TEKS.7.5.C solve mathematical and real-world problems involving similar shape and scale drawings.

TEKS.G.7.A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and

TEKS.7.5.A generalize the critical attributes of similarity, including ratios within and between similar shapes;

TEKS.G.3.C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and

IN.8.GM.5 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Describe a sequence that exhibits the similarity between two given similar figures.

VA.RLT.G.3.d determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

VA.MG.7.5 The student will solve problems, including practical problems, involving the relationship between corresponding sides and corresponding angles of similar quadrilaterals and triangles.

VA.MG.8.7.a given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and

VA.T.G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar.

FL.MAFS.8.G.1.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.