10D

Enlargements and similar figures

Enlargements and scale factors, similar figures, finding missing sides using the scale factor, and shadow problems.

Scale factor

$$k = \frac{\text{image length}}{\text{original length}}$$

$k > 1$ enlarges, $0 < k < 1$ reduces. Angles stay the same.

Scaling lengths

Every length is multiplied by the same scale factor.

Example 1●

A $3, 4, 5$ triangle is enlarged by scale factor $3$. Find the new sides.

$9, 12, 15$

Example 2●●

A $2$ m post casts a $3$ m shadow. At the same time a tree casts a $15$ m shadow. How tall is the tree?

The triangles are similar, with scale factor $15 \div 3 = 5$.

Tree $= 2 \times 5 = 10$ m

Flashcards

Scale factor

image ÷ original

Angles in similar figures

Equal

$k = 0.5$

Halves every length.

Practice

A $4$ cm side becomes $10$ cm. Scale factor?
A $2$ m post has a $3$ m shadow. A tree's shadow is $15$ m. Tree height in m?
A $3, 4, 5$ triangle is enlarged by factor $3$. Longest new side?
A $12$ cm side is reduced by scale factor $0.5$. New length?
Similar rectangles: $4 \times 6$ and $6 \times x$. Find $x$.
In similar figures, matching angles are:
A $9$ cm side becomes $3$ cm. Scale factor?
Triangles are similar with sides $4, 6$ and $10, x$ (matching in order). Find $x$.