Unit 7: Similarity Review

$$\frac{6}{25}$$

$$\frac{31}{15}$$

$$\frac{2}{3}$$

$$\frac{3}{2}$$

Rotation about (2, 3)

Reflection across line y = x

Dilation by factor 0.5

(4, 1)

(5, 0)

(3, 2)

(4, 3)

$$(x, y) \to (2x, 2y)$$

$$(x, y) \to (x, 2y)$$

$$(x, y) \to (2x, y)$$

$$(x, y) \to \left(\tfrac{x}{2}, \tfrac{y}{2}\right)$$

reflection

rotation

dilation

translation

dilation centered at O with scale factor 2, then translation left 1 and down 2; the triangles are similar

dilation centered at O with scale factor $$\tfrac{1}{2}$$ , then translation right 1 and up 3; the triangles are congruent

translation right 1 and up 3, then dilation centered at O with scale factor 2; the triangles are congruent

translation left 1 and down 2, then dilation centered at O with scale factor $$\tfrac{1}{2}$$ ; the triangles are similar

(−35, 13)

(−32, 12)

(−11, 4)

(−29, 7)

$$\dfrac{BC}{AB} = \dfrac{ED}{FE}$$

$$\dfrac{AB}{BC} = \dfrac{ED}{FE}$$

$$\dfrac{BE}{CD} = \dfrac{AF}{BE}$$

$$BE = \tfrac{1}{2}CD$$

A similarity transformation that maps one circle onto another must include a reflection.

There is no similarity transformation that will map one circle onto another.

All circles are similar.

ΔLMN ~ ΔL′M′N′

∠M ≅ ∠M′

MN ~ L′M′

∠L ≅ ∠L′

$$2\,LM = 3\,L′M′$$