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8. Similarity
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Math II

8.03 Similar figures

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Triangle ABC has been enlarged to triangle A'B'C'. What is the scale factor?

Two similar triangles, with the larger labeled A'B'C' and the smaller labeled ABC. These triangles are arranged such that the vertices B, B' and a point O are collinear. A thin line segment connects B passing through B' to point O. Similarly, the vertices C, C' and point O are collinear, and a thin line segment connects C passing through C' to point O. The line segments OB and BB' are each 7 units in length, making the total length of OB' 14 units. Similarly, the line segments OC and CC' are each 7 units, implying the total length of OC' is 14 units as well. The point O serves as the apex of two isosceles triangles, BOC and B'OC', with the base of each triangle formed by the vertices of the smaller and larger triangles, respectively.

$2$2

A

$\frac{1}{2}$12​

B

$3$3

C

$1$1

D
Easy
< 1min

Consider the following quadrilaterals.

Easy
< 1min

Which unit do we use to express the scale factor?

Easy
< 1min

Triangle A'B'C' has been reduced to form a smaller triangle ABC. What is the scale factor?

Easy
< 1min
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Outcomes

II.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.

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